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 of34mCl comes purely from (p, γ) cap-ture 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 em-ploying 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 indi-cate 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 of32,33,34S 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 AND34MCL 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
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 predomi-nantly during the opaque phase of the expanding ejecta. Furthermore, it has been cal-culated (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 tem-perature 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 iso-tope may go undetected unless there is a nearby ONe nova event (Leising and Clayton 1987). However, should it ever be detected, the subsequent34mCl 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)34Arand34mCl(p, γ)35Arreactions and nuclear core levels for the product nuclei within the energy range according to Figure1.4
33Cl(p, γ)34Ar
Resonance energyEr[keV] Level in34Ar [keV]
201 4865
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)vNaNX (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
·
"ma+mX 2πkBT
3/2
exp
−(ma+mX)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
≡NaNX· hσ(v)vi (2.4)
7
8 CHAPTER 2. THEORY Wherehσ(v)viis defined as the thermally averaged cross section,
hσ(v)vi= 4π
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.
Vcoul=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], 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, where E = 1/2µv2. In Equation 2.8, the function S(E)was introduced, which is called the "astro-physical 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=2πµZ2~1Z2e2 and equation2.9the factor,hσ(v)viof equation2.5, becomes
where E = 12µv2 was used to write the functions and integral in terms of the relative energy vari-able. 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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