Nuclear Physics I

Kern- und Teilchenphysik I Lecture 3: Liquid Drop Model

Prof. Nico Serra

Dr. Patrick Owen, Dr. Silva Coutinho

http://www.physik.uzh.ch/de/lehre/PHY211/HS2016.html

Nuclear Physics I

• Nuclear physics studies the nucleons interactions and the nuclei

• A particular configuration of nucleons in a bound state is called nuclide

• We indicate a nuclide with A nucleons and Z protons as ^A_ZX

• Two nuclides are called

– Isotopes is the have the same Z – Isobars is the have the same A

– Isotone is the have the same N = A Z

Definitions

- Light elements are created immediately after the big bang (Big Bang nucleosynthesis)

- Elements up to ⁵⁶Fe in star nuclear fusions (Stellar nucleosynthesis)

- Heavier elements in explosions of very heavy stars (Supernova nucleosynthesis)

Nuclear Abundance

• The mass of nuclides is given by M (A, Z) = N M_n + ZM_p B(A, Z)

• M_n is the mass of the neutron

• M_p is the mass of the proton

• B(A, Z) is the binding energy

• What keeps nucleons together is a remnant of the strong force

• E↵ective models are used to describe this interaction since in this regime we cannot make exact computations

Mass of Nuclides

Liquid Drop Model

B (A, Z ) = a

A

Volume term: Nucleons interact with the neighbouring nucleons only, the binding energy per nucleon inside the nuclide is constant (about 16MeV)

B (A, Z ) = a

A a

A

Surface term: Nucleons on the surface interact with less nucleons (~18MeV)

Liquid Drop Model

B (A, Z ) = a

A a

A

a

Z

A

Coulomb term: There is a repulsive term between all the protons. Each

proton interact with all the others (Z(Z-1)) and is inversely proportional to the radius A ^1/3 (aC ~ 0.7MeV )

Liquid Drop Model

B (A, Z ) = a

A a

A

a

Z

A

a

(A 2Z )

A

Asymmetry term: Nuclides that have similar number of protons and neutrons are more stable

Liquid Drop Model

B (A, Z ) = a

A a

A

a

Z

A

a

(A 2Z )

A (A, Z )

Pairing term: Even-even are more stables, then even-odd nuclides and then odd-odd nuclides

Liquid Drop Model

B (A, Z ) = a

A a

A

a

Z

A

a

(A 2Z )

A (A, Z )

8 >

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> >

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:

a

= 15.85M eV a

= 18.34M eV a

= 0.71M eV

a

= 23.21M eV (A, Z ) ⇠

8 >

<

>

+12M eV for even-even nuclides 0M eV for even-odd nuclides

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