Ion Optics Feasibility Study of the Astrophyscial 33,34m Cl(p, γ) Reactions at the CRYRING

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Ion Optics Feasibility Study of the Astrophyscial

33,34m Cl(p , γ ) Reactions at the CRYRING

Marius Anger 31st July 2017

Physic Department

Technische Universität München

Scientific work for obtaining the degree Bachelor of Science

Supervised by Prof. Dr. Shawn Bishop

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Abstract

This thesis is a feasibility study of the resonant ³³Cl(p, γ)³⁴Ar and ^34mCl(p, γ)³⁵Ar proton capture reactions, for stellar energies occurring in novae, at the new storage ring CRYRING at GSI. These reaction rates would be measured by detecting the yields of^34,35Ar fusion recoils exiting the CRYRING hydrogen gas jet target; thereby requiring particle identification detectors suitably positioned downstream of the target. The Rutherford elastic scattering yield, of the ^33,34mCl beam in the hydrogen gas target, arriving on such detectors must be severely limited in order to prevent destruction of the detectors and to prevent significant acquisition dead times. This study has therefore aimed at determ- ining the elastic yield contribution at three candidate detector positions downstream of the CRYRING target. We report that the position before the second quadrupole in section YR10 of the CRYRING has the lowest elastically scattered^33,34mCl yield and at the same time a good coverage of the^34,35Ar fusion products. All resonance energies of ³³Cl(p, γ)³⁴Arand ^34mCl(p, γ)³⁵Arare measurable, if the target density is adjusted.

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Acknowledgments

I would like to express my gratitude to my thesis supervisor Prof. Dr. Shawn Bishop for offering me this thesis topic and for guidance and support throughout the thesis. I’m particularly grateful for the opportunity to spend two weeks at GSI and one week at Russbach.

Also a big thanks goes to Jan Glorius, who got me well trained in MOCADI and C++. Also big thanks for being almost every time contactable via email or skype. I wish you and your family a good time with your kid.

Dr. Helmut Weick helped me and Jan to understand the special Mocadi code for CRYRING. Thanks for your help, too.

Last but not least I have to thank my fellow studentsMichael Engelhard andMoritz Sichert. They did help me to fix some issues in my code and with my computer.

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Introduction

1.1 Novae: Thermonuclear Run Away Sites

When a star initially forms from a collapsing molecular cloud in the interstellar medium, it contains primarily hydrogen and helium, with trace amounts of elements with atomic number greater than 2, which come from previous stellar explosion [1]. These elements are all uniformly mixed throughout the star. The star reaches the main sequence when the core reaches a temperature high enough to begin fusing hydrogen (∼5 MK) and establishes hydrostatic equilibrium.

Over its main sequence life, the star slowly converts the hydrogen in the core into helium: The proton- proton chain fuses four protons to one helium. Meanwhile the CNO-cycle is also producing helium by a sequence of(p, γ)reactions and beta decays starting with¹²C. The cycle eventually arrives at a(p, γ) reaction in ¹⁵N, leading to ¹⁶O·. Because ¹⁶O is an alpha-particle nucleus, the excitation energy at which it is produced is∼MeVhigher than the alpha-particle threshold in this nucleus. ¹⁶O· nucleus predominantly de-excites by emission of an alpha-particle. This(p, α) reaction then completes the cycle. Four protons are again converted into one alpha particle. When the star exhausts the hydrogen fuel in its core, nuclear reactions can no longer continue.

The core begins to contract, because the radiation pressure produced by the hydrogen fusion can no longer compete against gravity. This brings additional hydrogen from the outer layer into a zone where the temperature and pressure are adequate to cause fusion to resume in a shell around the core. The outer layers of the star then expand greatly due to radiation pressure, thus beginning the red-giant phase of the star’s life.

For stars of less than about 2 M [2] the core will become dense enough that electron degeneracy pressure will prevent it from collapsing further. Once the core is degenerate, it will continue to heat until it reaches a temperature of roughly10⁸K, hot enough to begin helium fusing via the triple-alpha process, where two alphas fuse to⁸Be and a third alpha then fuses⁸Be to ¹²C. ¹²C can further capture a alpha and produce¹⁶O. The helium fusion results in the build up of a carbon–oxygen core.

When the central helium is exhausted, the star collapses once again, causing helium in a outer shell to begin fusing. At the same time additional hydrogen may begin fusion in a shell just outside the burning helium shell. A star below∼8 M[3] will never start fusion in its degenerate carbon–oxygen core.

Instead, at the end of the burning phase the star will eject its outer layers, forming a planetary nebula with the core of the star exposed, ultimately becoming a white dwarf, with a size about our earth [4]

and a mass about0.6 M[5]. The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy. As a result, it cannot support itself by the fusion generated radiation pressure against gravitational collapse. It is supported only by electron degeneracy pressure, causing it to be extremely dense.

Approximately30 %of main sequence stars in our galaxy are observed to be within binary star systems [6]. In such a system one has two stars orbiting each other. In most cases the masses are different.

1

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2 CHAPTER 1. INTRODUCTION One star of the binary system will undergo the stellar evolution faster caused by its heavier mass: The gravitational force is larger and therefore more hydrogen has to be burned to hold up the radiation pressure. Thereby the core runs out of hydrogen faster and the stellar evolution is accelerated.

While one star has evolved to a white dwarf the other one is still in his red-giant phase. Material from the red giants outer shell (mostly composed of hydrogen) can now pass the so called Roche limit. It is the distance within which a celestial body will disintegrate due to a second celestial body’s tidal forces exceeding the first body’s gravitational self-attraction. The pulled material spirals down on the surface of the white dwarf. Conservation of angular momentum about the system’s center of mass causes the accreted material to form an accretion disk. The kinetic energy of the accreted material is thereby converted into heat. On the white dwarfs surface the material forms a hot, degenerate envelope surrounding the white dwarf [7]. An illustration and an observation of the Chandra telescope is shown in Figure1.1.

Figure 1.1: Left image [8]: Chandra image shows Mira A (right), a highly evolved red giant star, and Mira B (left), a white dwarf; right image [9]: an artist illustration of the same stellar object

As the white dwarf consists of degenerate matter the accreted hydrogen does not inflate for increasing temperatures. Eventually the temperature is high enough that proton capture reactions can occur in a thin radial layer at the interface between the base of the envelope and the surface. This will cause a drive up in temperatures in the burning zone. When the temperature reaches ∼50 MK, the nuclear energy generation is dominated entirely by CNO-cycle burning [10,11].

Now a thermonuclear runaway takes place: The CNO-cycle burning in combination with the degenerate matter rapidly drives up the temperature of the burning shell, without subsequent expansion and cooling as would be the case with an ideal gas. The degenerate conditions prevent an expansion.

Resonant proton-capture reactions onto the seed nuclei, that are now produced in the surface, begin to occur. These are explained in more detail in Chapter2. Such reactions can produce a high abundance fraction of nuclei between20≤A≤40.

Some 100 s to 1000 s later the degeneracy of the envelope is lifted, using 400 MK as the maximum temperature reached by Oxygen-Neon novae models. The temperature within the envelope exceeds the Fermi temperature of the degenerate matter and the envelope luminosity exceeds the Eddington luminosity limit, which is the maximum luminosity a star can reach with balance between radiation pressure and the gravitational force. This then causes the now non-degenerate system to behave like a ideal gas and pressure becomes temperature depended. The envelope explosively ejects the freshly forged elements into space [10, 12]. This is called anova. A recently observed nova, GK Persei, can be seen in Figure 1.2.

Only up to five percent of the accreted mass is fused during the power outburst [14]. So a white dwarf can potentially generate multiple novae over time as additional hydrogen continues to accrete onto its surface from the companion star. Eventually, the white dwarf could explode as a type Ia supernova, if it approaches the Chandrasekhar mass limit.

The total mass of ejected material in nova is10⁻⁴−10⁻⁵M [15]. Compared to the mass of a white dwarf (0.6 M) this is quite small. But the material contributes to the chemical enrichment of the interstellar medium. Observations of elemental abundances in the ejected shells can be used to test

Technische Universität München 2 Physics Department

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1.1. NOVAE: THERMONUCLEAR RUN AWAY SITES 3

Figure 1.2: GK Persei; image contains x-rays from Chandra X-Ray Telescope (blue), optical data from NASA’s Hubble Space Telescope (yellow), and radio data from the National Science Foundation’s Very Large Array (pink). The x-ray data show hot gas and the radio data show emissions from electrons that have been accelerated to extremely high energies by the nova shock wave. The optical data reveal clumps of material that were ejected in the nuclear explosion [13]

nova model predictions [7]. Such observations can be done by looking at the isotopic abundance fractions of presolar grains.

Physics Department 3 Technische Universität München

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4 CHAPTER 1. INTRODUCTION

1.2 Reactions with

³³

Cl and

^34m

Cl during Novae

Microscopic dust grains, produced around stars that existed before our solar system formed, can be extracted from meteorites, that have fallen to the Earth, and analyzed in terrestrial laboratories.

The stellar origin of this dust is revealed by its exotic composition, much different from that of the bulk of the material in the solar system. The nucleosynthesis in a presolar star makes a unique isotope composition of the different synthesized elements. These elements get blasted away by stellar explosions like a nova. The unique compositions can provide informations about specific astrophysical nuclear processes [16].

A possible characteristic of classical nova explosions on oxygen-neon white dwarfs [17,18] is coupled to the reaction network cycle of S, Cl and Ar shown in Figure1.3

852 The European Physical Journal Special Topics

Fig. 4.3. β-decay scheme for ³⁴Cl (Firestone 1996). The ^34mCl isomeric state at 146 keV decays into excited states of³⁴S producing three γ-rays of astronomical interest.β-decay branchings are given as percentages.

Fig. 4.4.The S-Cl burning cycle.β-decays are depicted with blue arrows and (p, γ) reactions are depicted with vertical red arrows. The cyclic nature is depicted by the thick outer red arrow for the (p, α) reaction on³⁵Cl.³⁴Cl is the relevantγ-ray emitter.

the production of the three astronomicalγ-ray lines [1.18 MeV (14%), 2.13 MeV (42%) and 3.30 MeV (12%)] arising from theβ-decay of^34mCl comes purely from (p, γ) capture on ³³S. Within these reaction paths the β-decay rates of ³³Cl and ³⁴Ar are both known (Endt and Firestone 1998); however, it must be stressed that both the

33Cl(p, γ)³⁴Ar isomeric-bypass reaction is entirely unknown at the present, as is the

34g,mCl(p, γ) (g = ground state) destruction rate. Both are presently modelled employing the Hauser-Feshbach statistical model for their reaction cross-sections. The level densities of both³⁴Ar and³⁵Ar, within the ONe-nova Gamow window, do not justify this treatment, as can be seen in Fig.4.5, where the vertical red bars indicate the Gamow window for the labelled temperature (in units of GK). Those states lying within the excitation energy range spanned by the 0.1 and 0.3 GK lines can contribute to resonant (p, γ) capture at ONe nova temperatures. Additionally, the

33S(p, γ)^34g,mCl reaction rate and the subsequent model yields of ^34mCl and ^34gCl will require revision owing to work done at the Maier Leibnitz Tandem Laboratory in Munich; seven new states within the Gamow window have been found in

Figure 1.3: The S-Cl burning cycle. β-decays are depicted with blue arrows and proton capture reactions(p, γ)are depicted with vertical red arrows. The cyclic nature is depicted by the thick outer red arrow for the (p, α)(proton capture with promptαemission) reaction on³⁵Cl [19]

By proton capture ³²S can react to ³³Cl and by a subsequent proton capture ³⁴Ar is produced:

33Cl(p, γ)³⁴Ar. Beta decay on both nuclei can take place and produce thereby ³³S and ³⁴Cl. The beta decay of ³⁴Ar to ³⁴Cl will populate the³⁴Cl ground state 100% of the time. By another proton capture ³³S can populate a isomeric first excited state of ³⁴Cl: ^34mCl. It has a lifetime of 32.00 min.

Through these sequences of (p, γ) reactions and beta decays, the cycle eventually arrives at a(p, γ) reaction in ³⁵Cl, leading to³⁶Ar·. Because³⁶Ar is an alpha-particle nucleus, the excitation energy at which it is produced is ∼MeVhigher than the alpha-particle threshold in this nucleus. As a result, the ³⁶Ar· nucleus predominantly de-excites by emission of an alpha-particle, rather than through a gamma-ray cascade to its ground state. This (p, α)reaction then completes the cycle.

33S and ³⁴S have been proposed to be an important isotope for the classification of presolar grains [20]. ^34mCl could be a potential target forγ-ray telescopes [21,22].

The abundance fractions of these species depend on the competition between their respective beta- decays and the reactions rates for

• ³³Cl(p, γ)³⁴Arand

• ^34mCl(p, γ)³⁵Ar

But these are currently unknown and this translates into uncertainties in the expected isotopic rations of^32,33,34S in presolar grains. The nuclear level schemes of³⁴Ar and³⁵Ar, showing the resonant states within the Gamow window at the expected temperatures of oxygen-neon novae can be seen in Figure

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1.2. REACTIONS WITH³³CL AND^34MCL DURING NOVAE 5 1.4. The vertical red bars to the right of each level scheme denote the span of the Gamow window for the corresponding labeled temperature (in units ofGK). The corresponding resonance energies are shown in table1.1.

These reactions are proposed to be measured at the CRYRING at the facility of the "Gesellschaft für Schwerionenforschung" (GSI) in Darmstadt, Germany [19]. This thesis will provide a feasibility study of this experiment by simulating the reactions inside the CRYRING sections YR09 and YR10 with MOCADI. For a detailed overview of the Experimental Facility and the simulation see Chapter3.

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6 CHAPTER 1. INTRODUCTION

Physics book: CRYRING@ESR 853

1/2+

(3/2,5/2)+

(3/2,5/2)+ (3/2,5/2)+

0.1

Cl + p 34

5591 6033 6258 6827

6631 6959

136 256 361 734 930 1062

35Ar

0.3 1.0

5897 5911

3 − 0 + 2 +

(5 )−

34Ar

Cl + p 33

4513 4631 4865 4967 5225 5310 5542 5620

303 201 561 650 878 956

0.1 0.3

1.0

4664

2 + 1 +

Fig. 4.5. Level schemes of³⁴Ar (Endt 1990) and³⁵Ar (Endt and Firestone 1998) showing the states of astrophysical interest along with their associated excitation energy, resonance energy and spin-parity assignments. The vertical red lines indicate the Gamow windows for (p, γ) capture with temperatures indicated in units of 10⁹K. The state atEx = 5225 keV in³⁴Ar is only tentatively assigned (Grawe et al. 1974). Spin-parity assignments are shown nested inside on the right, while resonance energies and excitation energies are, respectively shown on the outer left and outer right of each scheme.

34Cl (Parikh et al. 2009); their (p, γ) resonance strengths have yet to be determined.

Presently, their decay branchings into the ^34mCl isomeric state only have estimated upper limits, in terms of partial strengths (resonance strength times decay branch- ing), of∼1 meV (Freeman et al. 2011).

With its relatively short half-life of 32 min,^34mCl will undergoβ-decay predominantly during the opaque phase of the expanding ejecta. Furthermore, it has been calculated (Coc et al. 2000) that the isomeric level can be destroyed via photo-excitation to higher levels which subsequently branch, viaγ-decay, to the³⁴Cl ground state with larger branchings than that to return back to the isomer. This eﬀect is highly temperature dependent, with the result that the eﬀective ^34mCl half-life is reduced to

∼1 s at temperatures around 200 MK (Coc et al. 2000), greatly reducing the survival probability of this isotope into the ejecta phase (unless, of course, convection serves to transport a sizable fraction of it out of the peak temperature zone to the cooler surface zones of the envelope). Thus, it may well be that theγ-ray ﬂux from this isotope may go undetected unless there is a nearby ONe nova event (Leising and Clayton 1987). However, should it ever be detected, the subsequent^34mCl abundance derived therefrom could help, using a backward iterative method with nova models, to place empirical constraints on the maximum TNR temperature. But this possibility can only be meaningful with improved nova models in which the aforementioned (p, γ) reaction rates in this mass range are also improved.

Figure 1.4: Nuclear level scheme of ³³Cl(p, γ)³⁴Ar [23] and ³⁴Cl(p, γ)³⁵Ar [24] product nuclei in the range of the Gamow window (in red) for nova (0.1 GK), (0.3 GK) and X-ray bursts (1.0 GK) [19]

Table 1.1: Resonance energies for ³³Cl(p, γ)³⁴Arand^34mCl(p, γ)³⁵Arreactions and nuclear core levels for the product nuclei within the energy range according to Figure1.4

33Cl(p, γ)³⁴Ar

Resonance energyE_r[keV] Level in³⁴Ar [keV]

201 4865

303 4967

561 5225

646 5310

878 5542

956 5620

34mCl(p, γ)³⁵Ar

Resonance energyEr[keV] Level in³⁵Ar [keV]

110 6153

215 6258

588 6631

784 6827

916 6959

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Chapter 2

Theory

2.1 Thermonuclear Reaction Rates

Reaction rates can be measured by shooting an ion beam onto a suitable target. For a gas target with a number density NX, the total number of reactions per volume is σ(v)NX times the flux of incoming beam particlesa, whereσ(v)is the reaction cross section. The flux of beam particles that the target particles see is given by the number density of particlea, Na, times the relative velocity between particleaandb,v. In the center of mass frame of aandX, the reaction rate is given by

r=σ(v)vNaN_X (2.1)

wherev is the relative velocity betweenaand X. The respective velocity distributions of particlesa andX are each given by a Maxwell-Boltzmann distribution,

N(v)dv=N 2v²dv

(πm)^1/2(kBT)^3/2exp

− mv² 2kBT

(2.2) WherekB is the Boltzmann constant,mthe mass of the particle andN(v)dv the number density of all particles between momentumvanddv. The Maxwell-Boltzmann distribution in the center of mass system (CMS) between two particles is therefore

Na(~va) d³vaNX(~vX) d³vx=NaNX

·

"m_a+m_X 2πkBT

3/2

exp

−(ma+m_X)V² 2kBT

d³V

#

·

µ 2πkBT

exp

− µv² 2kBT

d³v

(2.3)

whereµis the reduced mass. By integrating equation2.3the reaction rateris given by

r=NaNX·4π µ

2πkBT

3/2Z ∞

0

vσ(v) exp

− µv² 2kBT

dv

≡N_aN_X· hσ(v)vi (2.4)

7

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8 CHAPTER 2. THEORY Wherehσ(v)viis defined as the thermally averaged cross section,

hσ(v)vi= 4π µ

2πkBT

3/2Z ∞

0

v³σ(v) exp

− µv² 2kBT

dv (2.5)

2.2 Non-resonant Reactions

The reaction rates of interest for this study are proton capture reactions. To evaluate equations2.4 and2.5, the cross section for the capture reaction is needed. At nova temperatures of ∼200 MK, the characteristic thermal kinetic energy iskBT, which is∼8.62·10⁻⁸keV. This is orders smaller than the height of the Coulomb barrier between a proton and nuclei with atomic numbers 16, 17, characteristic of S and Cl isotopes.

V_coul=Z₁Z₂e²

R =1.44·Z₁Z₂

R(fm) [MeV] (2.6)

whereZ1,Z2 are the coulomb charges of the reacting nuclei andeis the electron charge and Ris the distance between the two nuclei.

This corresponds to a low rate of particles that have enough energy to overcome the coulomb barrier.

The only way they can react is thereby by quantum tunneling which is given by the probability PP

[25],

P_P ∝exp

−2πZ1Z₂e²

~v

(2.7) wherevis the relative velocity andZ₁,Z₂are the coulomb charges of the reacting nuclei. Additionally the cross section σis proportional to a geometric factorπλ² withλthe de Broglie wavelength.

πλ²∝p⁻²∝E⁻¹ (2.8)

Combining the highly energy dependent terms of equations2.7and2.8, the cross section is paramet- erized by,

σ(E) =S(E)1 Eexp

−2πZ1Z₂e²

~v

=S(E)1 E exp

−2πZ1Z₂e²

~E^1/2

(2.9) where E = 1/2µv². In Equation 2.8, the function S(E)was introduced, which is called the "astrophysical S-factor". It is assumed to be a weakly dependent function of energy, because at low energy, charged particle cross sections are dominated by the highly energy-sensitive tunneling term and the E⁻¹term. Withb=^2πµZ_2~¹^Z²^e² and equation2.9the factor,hσ(v)viof equation2.5, becomes

hσ(v)vi= Z ∞

0

σ(E)v(E)Φ(E)dE

= 8

µπ 3/2

√1 kBT

Z ∞

0

S(E) exp E

kBT ·bE^−1/2

dE (2.10)

where E = ¹₂µv² was used to write the functions and integral in terms of the relative energy variable. The integral is mostly dominated by the exponential factors, because S(E)is a weakly varying function of energy. The exponential function in the integral is the product of the Maxwell-Boltzmann

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2.2. NON-RESONANT REACTIONS 9

Abbildung 5.2: Dieser Graph zeigt das Maximum des Integrals (5.20) f¨ur konstantes S(E). Bild entnommen aus [1].

da die meisten Kernreaktionen auf der ”Flanke” einer Resonanz stattfinden wie zum Beispiel die Reaktion

14

7 N+p→¹⁵8 O (5.22)

aus dem CNO-Zyklus. Dies ist in Abb. 5.3 dargestellt. Falls die Resonanz in die Nähe des Gamow-Peaks kommt, muss deren Beitrag zu (5.20) berücksichtigt werden und S(E) ist nicht mehr konstant. Für geringere Energien werden die Resonanzpeaks im Allgemeinen schmäler und kleiner.

Wenn man nun all diese Ergebnisse mit experimentellen Beobachtungen im Plasmen vergleicht, stellt man fest, dass man die Reaktionsrate, unabh¨angig von den Details des Prozesses, immer untersch¨atzt. Dieser Fehler kommt daher, weil bisher davon ausgegangen wurde, dass in einem Sternplasma nur Atomkerne vorhanden sind.

Tatsächlich sind aber noch die Elektronen der Atomhüllen da, weil ein Stern ja in etwa elektrisch neutral ist. Die negative Ladung der Elektronen bewirkt eine Abschirmung des positiven Potentials der Kerne und verringert so die Coulomb- Barriere. Dies führt dann zu einer höheren Reaktionsrate. Auch wenn der Effekt dieses sog. Debye-Shielding nicht allzu stark ist, sei er der Vollständigkeit halber hier erwähnt.

28

Figure 2.1: Exponential factors of equation 2.10 and resulting "Gamow window" (dashed) with a temperature of1 keVto3 keV, where the peak is15 keVto20 keV[26]

distribution and the tunneling factor, and is called the Gamow window. It is shown schematically in Figure2.1with the dashed curve.

If the S-Factor,S(E), is only weakly depending on the energy within the Gamow window, it can be treated as a constant. The Gamow window can then be approximated by a Gaussian function. The result is [27],

exp E

k_BT ·bE^−1/2

= exp

− E

k_BT · −bE^−1/2

≈Cexp −E−E₀

∆ 2

!2

(2.11)

where the constant,C, and the width at half maximum∆ are defined as [27]

C= exp E0

kBT ·bE₀^−1/2

= exp

−3E0

kBT

≡exp(−τ) (2.12)

∆ = 4

√3

pE₀kBT = 0.75· Z₁²Z₂²µT₆⁵^1/6

[keV] (2.13)

These can also be seen in Figure 2.2 as the dotted line, where the solid line is the exact Gamow window.

The maximum of the Gaussian,E0, is given by [27]

E0= bk_BT

2 2/3

= 1.220· Z₁²Z₂²µT₆²1/3

[keV] (2.14)

whereTn=T /10ⁿ, with T in kelvin. In the most cases the approximation with a Gaussian function holds quite well.

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10 CHAPTER 2. THEORY

3.2 Nonresonant and Resonant Thermonuclear Reaction Rates 167

10⁻²

10⁻⁶

10⁻¹⁰

10⁻¹⁴

10⁻¹⁸

10⁻²²

10⁻²⁶

10⁻³⁰

E₀= 0.32 MeV

kT

Exact Approx.

(a)

(b)

0 2

1.5

1

0.5

0

0.2 0.4 0.6 0.8 1 1.2

0 0.2 0.4 0.6 Energy (MeV) e^–E/kTe⁻^2πη e^–E/kT

e^−2πη

0.8 1 1.2

Probability (arb. units)Probability (arb. units)

Figure 3.13 (a) Maxwell–Boltzmann factor (e^−E∕kT; dashed line) and Gamow factor (e⁻²^𝜋𝜂; dashed-dotted line) versus energy for the ¹²C(𝛼,𝛾)¹⁶O reaction at a temperature of T =0.2 GK. The producte^−E∕kTe⁻²^𝜋𝜂, referred to as theGamow peak, is shown as solid line.

(b) The same Gamow peak shown on a linear

scale (solid line). The maximum occurs at E₀ =0.32 MeV while the maximum of the Maxwell–Boltzmann distribution is located at kT=0.017 MeV (arrow). The dotted line shows the Gaussian approximation of the Gamow peak.

where in the numerical expression M

_i

are the relative atomic masses of projectile and target in units of u.

The energy E

₀

is the most eﬀective energy for nonresonant thermonuclear reactions. Figure 3.14 shows the Gamow peak energy E

₀

versus temperature for a number of proton- and α -particle-induced reactions. The Gamow peak energy increases with increasing target–projectile charge. The open circles indicate the height V

_C

of the Coulomb barrier. Notice that, except for the highest temperatures near T = 10 GK, we ﬁnd E

₀

≪ V

_C

and thus the interacting charged nuclei must always tunnel through the Coulomb barrier.

Figure 3.15 shows the Gamow peak at a temperature of T = 30 MK for three reactions: (i) p + p, (ii)

¹²

C + p, and (iii)

¹²

C + 𝛼 . It demonstrates a crucial aspect

Figure 2.2: The Gamow peak for the ¹²C(α, γ)¹⁶O reaction at a temperature of 0.2 GK shown on a linear scale (solid line). The maximum occurs at E₀ = 0.32 MeV while the maximum of the Maxwell–Boltzmann distribution is located at kT = 0.017 MeV (arrow). The dotted line shows the Gaussian approximation of the Gamow window [27]

2.3 Resonant Reactions

Earlier S(E) was assumed as a function that is not strongly changing with reasonable changes in energy. Over the width of the Gamow window, it is constant, or linear in energy with a very small slope. But if a isolated discrete excited state in the product nucleus is inside the Gamow window range of relative energy (Er≈E₀), this assumption is wrong. In this case the reaction occurs in two steps.

X+a→C→Y +b (2.15)

The reactants build a compound nucleus and this decays rapidly into the products. The probability that X reacts toY is given by

P(X →Y) =P(X →C)·P(C→Y) (2.16)

The reaction rate for process with mean lifetimeτ is given by ri= 1

τi

= Γi

~

(2.17) where Γi is the width of the resonance.

So the total destruction rate of the compound nucleus Cin iindependent processes is given by

r=X

i

ri= 1

~ X

i

Γi≡ Γ

~ (2.18)

If a reaction occurs with particle a, the cross sectionσ ∼Γa and the probability for the decay into outgoing channelbis therefore∼Γb/Γ. The cross section is thereby given as

σ∼ΓaΓb

Γ ·P(E) (2.19)

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2.4. ION OPTICS 11 WhereP(E)is the Breit-Wigner-formula for resonances:

P(E) = Γ

(E−Er)²+ (Γ/2)² (2.20)

The resonance energy is given byEr.

It is now possible to plot the resonance strength and the width at half maximum ∆ of the Gamow window at different temperatures side by side with the nuclear core level scheme of the product nuclei.

2.4 Ion Optics

The general task in beam optics is to transport charged particles from point A to point B along a desired path. The collection of bending and focusing magnets installed along this ideal path are called the magnet lattice and the complete optical system including the bending and focusing parameters is called a beam transport system (see also [28]).

2.4.1 Particle Beam Guidance

To guide a charged particle along a predefined path, magnetic fields are used which deflect particles as determined by the equilibrium of the centrifugal force and Lorentz force

mγv²~k+q

~ v×B~

= 0 (2.21)

where~k= (kx, k_y,0) is the local curvature vector of the trajectory, which is pointing in the direction of the centrifugal force. Assuming that the magnetic field vectorB~ is oriented normal to the velocity vector~v, the treatment of linear beam dynamics is restricted to purely transverse fields. This has no fundamental reason other than to simplify the formulation of particle beam dynamics. The transverse components of the particle velocities for relativistic beams are small compared to the particle velocity.

A curvilinear coordinate system(x, y, z)following the ideal path is used. The direction of the particle is denoted with the coordinates: The bending radius for the particle trajectory in a magnetic field is from equation2.21withp=γmv

~kx,y=±qc βE

B~y,x (2.22)

and the angular frequency of revolution of a particle on a complete orbit normal to the fieldB is ωL=

qc EB

(2.23)

which is also called the cyclotron or Larmor frequency. The sign in equation2.22has been chosen to meet the definition of curvature in analytical geometry, where the curvature is negative, if the tangent to the trajectory rotates counterclockwise. Often, the beam rigidity, defined as

|Bρ|= p0

q (2.24)

is used to normalize the magnet strength. Using more practical units the expressions for the beam rigidity and bending radius become

Bρ[Tm] = 10

2.998βE[GeV] (2.25)

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and

1

ρ[m⁻¹] = B

Bρ= 0.2998Z A

|B[T]|

βE[GeV/u] (2.26)

where the sign for the bending radius was dropped. For relativistic particles this expression is further simplified sinceβ ≈1. The deflection angle in a magnetic field is

θ= Z dz

ρ (2.27)

or for a uniform field like in a dipole magnet of arc length l_m the deflection angle isθ=l_m/ρ.

2.4.2 Particle Beam Focusing

Similar to the properties of light rays, particle beams also have a tendency to spread out due to an inherent beam divergence. To keep the particle beam together and to generate specifically desired beam properties at selected points along the beam transport line, focusing devices are required. Any magnetic field, that deflects a particle by an angle proportional to its distance r from the axis of the focusing device, will act in the same way as a glass lens does in the approximation of paraxial, geometric optics for visible light. Iff is the focal length, the deflection angleαis defined by

α=−r

f (2.28)

A similar focusing property can be provided for charged particle beams by the use of azimuthal magnetic fieldsBφ with the property

α=−l

ρ =−qc

βEBφl=−qc

βEgrl (2.29)

wherelis the path length of the particle trajectory in the magnetic fieldBφandgis the field gradient defined by B_φ=gr or byg= dB_φ/dr.

In beam dynamics, it is customary to define an energy independent focusing strength. Similar to the definition of the bending curvature a focusing strengthK is define by

K= q pg= qc

βEg (2.30)

2.4.3 Equation of Motion

Magnetic fields are used to guide charged particles along a prescribed path or at least keep them close by. This path, or reference trajectory, is defined geometrically by straight sections and bending magnets only. Dipole magnets deflect the path and quadrupole and higher order magnets do not influence this path but provide the focusing forces necessary to keep all particles close to the reference path.

The most convenient coordinate system to describe particle motion is the curvilinear coordinate system as seen in Figure 2.3. The curvatures are functions of the coordinate z and are nonzero only where there are bending magnets. The equations of motion are derived in the horizontal plane only. The generalization to both horizontal and vertical plane is straightforward. Using the notation of Figure 2.4 the deflection angle of the ideal path is dφ0 = dz/ρ0 or utilizing the curvature to preserve the directionality of the deflection

dφ0= +k0dz (2.31)

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2.4. ION OPTICS 13

“chap02” — 2003/6/28 — page 33 — #4

2.2 Circular accelerator 33

R

x s

y Fig. 2.3 Locally defined right-handed

coordinate system used with bending design.

Here s is the distance along the design orbit, x is the distance from this orbit along the radius of curvature, and y is the distance from the design orbit out of the bend plane.

along the trajectory are a superposition of angle and offset perturbations. From these observations, we may strongly suspect that the perturbed trajectory is a harmonic oscillation, but we must first develop the proper analysis tools to verify this suspicion.

As stated in Chapter 1, as we will typically take the distance along the design orbit to be the independent variable (in this case indicated by

s), we implicitly

wish to analyze the charged particle dynamics near the design orbit. In the present case, this orbit is specified by a certain radius of curvature

R

(and thus a certain momentum

p₀ = qB₀R), and center of curvature,(x₀

,

y₀)

. With this choice of analysis geometry, we can locally define a new right-handed coordinate system

(x,y,s), as shown in Fig. 2.3. In this coordinate system, x

is the distance of the orbit under consideration from the design orbit, in the direction measured along the radius and normal to

s. The distancey

(formerly indicated by the coordinate

z

in Section 2.1) is measured from the design orbit

to the particle orbit under consideration, in the direction out of the bend plane.

¹ ¹This convention, in which the symboly is defined to be the distance out of the bend plane is typical of the American literature. European beam physicists more often use the symbolz instead, but we do not follow this convention even though it connects more naturally to our previous discussion. This is because our adopted convention makes subsequent derivations somewhat easier to understand, and also because it allows the connection between linear accelerator and circular accelerator coordinate systems to become more obvious.

The choice of a right-handed system in this case is a function of the direction of the bend, and in simple circular accelerators, one is free to construct the curvilinear coordinates once and for all. On the other hand, when we encounter bends in the opposing direction, as in chicane systems (see Chapter 3), we will choose to consistently define the coordinate

x, so that it is positive along

the direction away from the origin of the bend. As we will also choose to leave the vertical direction unchanged in this transformation, a left-handed coordinate system will result when the bend direction is changed.

The coordinate system shown in Fig. 2.3 is quite similar to a cylindrical coordinate system, with

x

related to the radial variable

ρ

by the definition

x≡ρ−R,s

replacing the azimuthal angle

φ (

ds

=R

d

φ)

, and

y, as previously

noted, replacing

z. Thus we can write the equations of motion for orbits in this

system by using the Lagrange–Euler formulation (see Problem 2.1), as

dp

_ρ

dt

= γm₀v²_φ

ρ −qv_φB₀

, (2.9)

where

v_φ =ρφ˙

is the azimuthal velocity.

Equation (2.9) can be cast as a familiar differential equation by using

x

as a small variable (x

R, which is also equivalent, as will be seen below, to

the paraxial ray approximation) to linearize the relation. This is accomplished through use of a lowest order Taylor series expansion of the motion about the design orbit equilibrium

(px =p_ρ =

0) at

ρ =R,

dp

x

dt

∼= −γ0m₀v²₀

R² x.

(2.10)

Figure 2.3: Locally defined right-handed coordinate system used with bending design. Heresis the distance along the design orbit,xis the distance from this orbit along the radius of curvature, andy is the distance from the design orbit out of the bend plane. [29]

5.3 Equation of Motion 107

Fig. 5.4 Particle trajectories in deﬂecting systems.

Reference pathzand

individual particle trajectorys have in general different bending radii

dz

ρ₀

d

_ϕ

u ds

individual particle trajectory

dϕ₀ ρ

reference path

The ideal curvature 0 is evaluated along the reference trajectory u D 0 for a particle with the ideal momentum. In linear approximation with respect to the coordinates the path length element for an arbitrary trajectory is

dsD.1C0u/dzCO.2/; (5.22) where u D x or y is the distance of the particle trajectory from the reference trajectory in the deﬂecting plane.

The magnetic fields depend onzin such a way that the fields are zero in magnet free sections and assume a constant value within the magnets. This assumption results in a step function distribution of the magnetic fields and is referred to as the hard edge model, generally used in beam dynamics. The path is therefore composed of a series of segments with constant curvatures. To obtain the equations of motion with respect to the ideal path we subtract from the curvature for an individual particle the curvature0of the ideal path at the same location.

Sinceuis the deviation of a particle from the ideal path, we get for the equation of motion in the deﬂecting plane with respect to the ideal path from Fig.5.4 and (5.20), (5.21) withu⁰⁰D .d'=dzd'0=dz/,

u⁰⁰ D .1C0u/C0; (5.23)

where the derivations are taken with respect to z. In particle beam dynamics, we generally assume paraxial beams,u⁰² 1since the divergence of the trajectories u⁰ is typically of the order of 10³ rad or less and terms in u⁰² can therefore be neglected. Where this assumption leads to intolerable inaccuracies the equation of motion must be modiﬁed accordingly.

The equation of motion for charged particles in electromagnetic fields can be derived from (5.23) and the Lorentz force. In case of horizontal deflection, the curvature is D x and expressing the general field by its components, we have

Figure 2.4: Particle trajectories in deflecting systems. Reference pathz and individual particle tra- jectoryshave in general different bending radii [28]

wherek₀ is the curvature of the ideal path. The deflection angle for an arbitrary trajectory is then given by

dφ= +kds (2.32)

The ideal curvaturek₀is evaluated along the reference trajectory u= 0for a particle with the ideal momentum. In linear approximation with respect to the coordinates the path length element for an arbitrary trajectory is

ds= (1 +k0u)dz+O(2), (2.33)

whereu=xoryis the distance of the particle trajectory from the reference trajectory in the deflecting plane.

The magnetic fields depend onz in such a way that the fields are zero in magnet free sections and assume a constant value within the magnets. This assumption results in a step function distribution of the magnetic fields and is referred to as the hard edge model, generally used in beam dynamics. The path is therefore composed of a series of segments with constant curvatures. To obtain the equations of motion with respect to the ideal path the curvaturek₀ of the ideal path is subtracted from the

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14 CHAPTER 2. THEORY curvaturekfor an individual particle at the same location. Sinceuis the deviation of a particle from the ideal path, for the equation of motion in the deflecting plane with respect to the ideal path from Figure2.4 and equation2.31,2.32withu⁰⁰=−(dφ/dz−dφ0/dz),

u⁰⁰=−(1 +k0u)k+k0 (2.34)

where the derivations are taken with respect to z. Paraxial beams were assumed, u⁰² 1, since the divergence of the trajectoriesu⁰ is typically of the order of10⁻³rad or less and terms inu⁰² can therefore be neglected. Where this assumption leads to intolerable inaccuracies the equation of motion must be modified accordingly.

The equation of motion for charged particles in electromagnetic fields can be derived from equation 2.34 and the Lorentz force. In case of horizontal deflection, the curvature isk =k_x and expressing the general field by its components with equation 2.22

k_x= 1 1 +δ

k₀_x+Kx+1 2mx²

(2.35)

where the field is expanded into components up to second order. The three lowest order multipoles, a bending magnet, a quadrupole and a sextupole were used. A real particle beam is never monochromatic and therefore effects due to small momentum errors must be considered. This can be done by expanding the particle momentum in the vicinity of the ideal momentump0

1

p= 1

p₀(1 +δ)≈ 1

p₀(1−δ+. . .) (2.36) The horizontal plane (u=xand k=kx) is now applied to equation 2.34to get with equation 2.35 and2.36the equation of motion

x⁰⁰+ (K+k²₀_x)x=k0x(δ−δ²) + (K+k²₀_x)xδ−1

2mx²−k0Kx²+O(3) (2.37) The definitions of energy independent field strength parameters as defined in equation 2.30and2.22 was used. The equation of motion in the vertical plane can be derived in a similar way by setting u=y in equation2.34andk=ky. The equation of motion in the vertical plane thereby is

y⁰⁰−(K−k₀²_y)y=k₀_y(δ−δ²)−(K−k²₀_y)yδ+1

2my²+k₀Ky²+O(3) (2.38)

2.4.4 Solutions for the linear Equations of Motion

Equations 2.37 and 2.38 are the equations of motion for strong focusing beam transport systems, where the magnitude of the focusing strength is a free parameter. No general analytical solutions are available for arbitrary distributions of magnets. The best tool in the mathematical formulation of a solution to the equations of motion is the ability of magnet builders and alignment specialists to build magnets with almost ideal field properties and to place them precisely along a predefined ideal path.

In addition, the capability to produce almost monochromatic particle beams is of great importance for the determination of the properties of particle beams. As a consequence, all terms on the right-hand side of 2.37and 2.38can and will be treated as small perturbations and mathematical perturbation methods can be employed to describe the effects of these perturbations on particle motion.

The left-hand side of the equations of motion resembles that of a harmonic oscillator although with a time dependent frequency. By a proper transformation of the variables equations2.37and2.38can be expressed exactly in the form of the equation for a harmonic oscillator with constant frequency.

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2.5. DIRECTION COSINES AS A BEAM PROPERTY 15 To solve the equations of motion2.37and2.38, the homogeneous differential equations are solved

u⁰⁰+Du= 0, (2.39)

whereustands forxoryand whereDis a constant withD=K+k²₀_xorD=−(K−k₀²

y), respectively.

The principal solutions of this differential equation are forD >0:

C(z) = cos√ Dz

S(z) = 1

√Dsin√ Dz

(2.40) and forD <0:

C(z) = coshp

|D|z

S(z) = 1

p|D|sinhp

|D|z

(2.41)

2.4.5 Matrix Formulation

The solution2.40and2.40of the equation of motion may be expressed in matrix formulation u(z)

u⁰(z)

=

C(z) S(z) C⁰(z) S⁰(z)

u₀ u⁰₀

(2.42) The principal solutions can be calculated for individual magnets, a transformation matrix for each individual element of the beam transport system can be obtained.

2.5 Direction Cosines as a Beam Property

Ifvis a vector in three-dimensional space (R³) then

~v=v_x~e_x+v_y~e_y+v_z~e_z (2.43) wheree_x,e_y,e_zare the unit vectors in x, yandz. The direction cosines are therefore:

α= cos(a) =~v·~e_x

k~vk = v_x qv_x²+v_y²+v_z²

(2.44)

β = cos(b) =~v·~ey

k~vk = vy

q

v²_x+v²_y+v_z²

(2.45)

γ= cos(c) =~v·~ez

k~vk = vz

q

v_x²+v_y²+v_z²

(2.46)

witha,bandcthe direction angles of the vectorvand the unit vectors. These equations can be seen in a graphical presentation in Figure2.5. α, β andγare the so called direction cosines.

These direction cosines can be applied to the momentum vector of the particles. The momentum is saved as variablea and b inside MOCADI. These are defined as angles towards the beam axis and have to be converted to direction cosine angles

α=tan(a)

1000 (2.47)

β =tan(b)

1000 (2.48)

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v

x

e

x

v

z

e

z

v

y

e

y

b c a

(a) Unit vectorvinR³

v

e

x

e

_z

e

_y

| v |

b c

a

(b) Direction cosines and direction angles for the unit vectorv

Figure 2.5: Illustrations of the vectorv direction cosine representation [30]

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Chapter 3

Experimental Facility and Ion Optics Simulation

The measurement of the reaction rate of ³³Cl(p, γ)³⁴Ar and ^34mCl(p, γ)³⁵Ar are proposed to be at CRYRING at the GSI in Darmstadt [19]. The following section gives a short overview of the facility.

Furthermore the simulation and analysis is described in section3.2.1and3.2.2.

3.1 CRYRING at GSI

Figure3.1shows a complete map of todays setup and the future setup of the FAIR collaboration.

the decay of nuclear states by Internal Conversion (IC) [137].

So far, no experimental evidence has been reported for NEEC.

The combination of the ESR and the CRYRING is ideally suited for investigations of astrophysical capture reactions. The p-process Gamow window for capture reactions on nuclei in the tin region at T

₉

= 2 − 3 is E

_Gamow

= 1 . 8 − 4 . 5 MeV for proton- and 5.3 − 10.3 MeV for α-induced reactions, which are perfectly within the energy range of the CRYRING [138, 139]. These ex- periments, however, require the installation of particle detectors inside the ultra-high vacuum of the ring. The development of the corresponding detectors is ongoing. Furthermore, reactions of interest for the rp-process might be possible to address. Last but not least, also a wide range of nuclear reaction measure- ments profiting from cooled low-energy radioactive beams is planned in a programme that is complementary to the studies envisioned by the EXL collaboration at higher beam energies (see Section 4.4.2).

4.4. Storage Rings at FAIR

A complex of several storage rings is planned at the future FAIR facility which is schematically illustrated in Figure 11.

Present GSI facility

Future FAIR facility

Figure 11: A schematic view of the Facility for Antiproton and Ion Research in Darmstadt. The present GSI facility consisting of the UNILAC, SIS, FRS and ESR is shown together with the location of the CRYRING which is presently being reassembled.

It is proposed to extend the existing GSI facility by adding the heavy-ion synchrotrons SIS-100 and SIS-300, a two-stage large-acceptance superconducting fragment separator Super- FRS [140] and a dedicated complex of storage rings (the Col- lector Ring (CR), the Recuperated Experimental Storage Ring (RESR), the New Experimental Storage Ring (NESR), and the High-Energy Storage Ring (HESR)) [141].

It is envisioned that secondary beam intensities will be supe- rior by about 4 orders of magnitude compared to those presently available. The exotic nuclei separated in-flight by the Super- FRS will be stochastically pre-cooled in the CR and transported via RESR to the NESR or HESR for in-ring experiments. How- ever, FAIR will be realised in stages, which are defined by the Modularised Start Version of FAIR (MSV) [142]. The RESR and NESR rings are not part of the MSV and shall be con- structed at a significantly later stage. Due to the MSV, the fa-

cility design was modified to enable its operation also without these rings. One of the consequences was that the present ESR will stay in operation until it is replaced by the NESR. In addi- tion, see Fig. 1, the CRYRING, which was moved from Stock- holm University to GSI, will be installed behind the ESR [31].

A beam line connecting the Super-FRS via CR with the ESR is envisaged as an extension of the MSV of FAIR. If con- structed, it will be possible to study the most exotic nuclei pro- vided by the Super-FRS also with detection setups at the ESR- CRYRING. The experimental conditions at FAIR will substan- tially improve qualitatively and quantitatively the research po- tential on the physics of exotic nuclei, and will allow for ex- ploring new regions in the chart of the nuclides, of high interest for nuclear structure and astrophysics. Several scientific pro- grammes are put forward at FAIR and are discussed in the fol- lowing.

4.4.1. ILIMA: Isomeric beams, LIfetimes and MAsses

The ILIMA project is based on the successful mass and half- life measurements at the present ESR. The key facility here will be the CR, which is particularly designed for conducting IMS measurements [143]. The ion-optical matching of the Super- FRS and the CR will provide a close to unity transmission of the secondary beams. The CR will be equipped with two time- of-flight (ToF) detectors installed in one of the straight sec- tions, which will enable in-ring velocity measurement of each particle. The latter is indispensable for correction of the non- isochronicity (see [36, 144]). Employing the novel resonant Schottky detectors [145] will enable simultaneous broad-band mapping of nuclear masses and lifetimes by the SMS technique.

In addition, heavy-ion detectors will be installed after dipole magnets in the CR. The mass surface that will become acces- sible in the CR is illustrated in Figure 6, where the smallest production rate of one stored ion per day is assumed.

In addition to the experiments in the CR, there are plans to use the CRYRING and the HESR. It is proposed to search for the NEEC process in the former, whereas the accumulation scheme in the latter will be used to achieve high intensities of long-lived highly-charged radionuclides. One striking example to be addressed is the measurement of the bound-state β

⁻

-decay of

²⁰⁵

Tl [146] (predicted T

1/2

≈ 1 year), which is important for solar neutrino physics and astrophysics.

4.4.2. EXL: EXotic nuclei studied in Light-ion induced reac- tions at the NESR storage ring

The objective of the EXL-project, is to capitalise on light- ion induced direct reactions in inverse kinematics [21, 22]. Due to their spin-isospin selectivity, light-ion induced direct reac- tions at intermediate to high energies are an indispensable tool in nuclear structure investigations. For many cases of direct reactions the essential nuclear structure information is deduced from high-resolution measurements at low-momentum transfer.

This is in particular true for example for the investigation of nu- clear matter distributions by elastic proton scattering at low q, for the investigation of giant monopole resonances by inelastic scattering at low q, and for the investigation of Gamow-Teller transitions by charge exchange reactions at low q. Because of 11

Figure 3.1: A schematic view of the Facility for Antiproton and Ion Research in Darmstadt. The present GSI facility consisting of the UNILAC, SIS, FRS and ESR is shown together with the location of the CRYRING which is presently being commissioned [31].

17

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18 CHAPTER 3. EXPERIMENTAL FACILITY AND ION OPTICS SIMULATION For an experiment at the CRYRING firstly an ion beam will be produced and preaccelerated in the UNILAC. This is followed by an acceleration to full energy (e.g. 600^MeV_u ) in the SIS-18, from where the beam is send to the fragment separator (FRS). At the production target, the ion beam induces fragmentation reactions on the target nuclei, thereby producing a cocktail of various radioactive nuclei.

The kinematics of the fragmentation reaction direct the cocktail beam of radioactive nuclei through the fragmentation separator. The FRS then separates out of the cocktail beam a specific nuclei, of the experimenter’s choice. This beam is then further send to the experimental storage ring (ESR) to be cooled and then send to the CRYRING. Here it can be cooled further. The ions can revolve at 100 kHzto1000 kHzin the ring.

Figure3.2shows a plan view of the CRYRING. The ion beam from the ESR is injected into the YR01 section of the ring, via the beamline (green) in the top left corner of 3.2. The ring consists of 12 sections. Between every section is a dipole magnet which bends the beam about 30^◦. Every second section is a focusing section with three quadrupole and two hexapole magnets. At section YR03 the electron cooler is placed. The target will be placed in section YR09.Physics book: CRYRING@ESR 803

Fig. 1.3. Top view of the CRYRING model in the new CRYRING@ESR conﬁguration.

Labels indicate the section numbering and the dominant functions of each straight section.

Please see text for a further description.

depending on ion energy and charge state. Besides ion injection from ESR, a local injector beamline is prepared, which allows for continued service even at times, where major shutdowns of the GSI accelerators is e.g. a necessity of FAIR construction. The local injector is equipped with a 300 keV/u RFQ (for m/q ≤ 2.85) and a limited reach of available ion species, depending on compatible ion sources.

In the following chapters we sketch out a broad scientific program in the fields of atomic and nuclear physics and at their intersection. The realization will allow for exciting high-precision spectroscopy studies of atomic systems and their dynamics where special emphasis is given to the effects of quantum electrodynamics (QED) and electron-correlation in the strong field domain (Chap. 2). Here, also the intersection of atomic and nuclear physics is addressed where the imprint of nuclear effects on the electronic shell are investigated with spectroscopic methods (Chap. 3), and exploring the nuclear structure, nuclear dynamical processes and quantitative measurements of astrophysically relevant (p, γ)-reaction rates (Chap. 4). These experiments are of prime interest for testing modern theoretical methods on fundamental processes as well as for applications in astrophysics and for modelling plasmas. In the domain of slow collisions in of heavy ions at highest charge-states where atomic processes are prevailed by large perturbations, these studies are expected to refine sub- stantially our understanding of the physics of extreme electromagnetic fields. Also, CRYRING@ESR will offer extracted high-quality ion beams, thus enabling novel Figure 3.2: Top view of the CRYRING model in the new CRYRING@ESR configuration. Labels indicate the section numbering and the dominant functions of each straight section. [19]

Ion Optics Feasibility Study of the Astrophyscial 33,34m Cl(p, γ) Reactions at the CRYRING