Nuclear Models — Question 3

Question 3

The mass formula combines competing contributions to binding

Use the supplied model $B=a_vA-a_sA^{2/3}-a_cZ(Z-1)A^{-1/3}-a_a(A-2Z)^2/A+\delta$. Coefficients are $a_v=15.5$, $a_s=17.0$, $a_c=.700$, $a_a=23.0$ in MeV. For even-even nuclei take $\delta=12/\sqrt A$ MeV. Consider A=64, Z=28.

1. Evaluate the volume, surface, Coulomb, asymmetry and pairing terms.

2. Find total binding and binding per nucleon, and quantify how much the asymmetry term lowers B.

Question 3 - Solution

The mass formula combines competing contributions to binding

(a) Method and calculation

$$\boxed{B_v=992,\quad B_s=-272,\quad B_C=-.700(28)(27)/4=-132.3\,\mathrm{MeV}}.$$$$\boxed{B_a=-23(64-56)^2/64=-23.0\,\mathrm{MeV},\quad\delta=+1.50\,\mathrm{MeV}}.$$

(b) Interpretation and further calculation

$$\boxed{B=992-272-132.3-23.0+1.50=566.2\,\mathrm{MeV}}.$$$$\boxed{B/A=8.8469\,\mathrm{MeV},\quad|B_a|=23.0\,\mathrm{MeV}}.$$

Physical check

The coefficients define an illustrative smooth model, not a precision empirical mass prediction. Shell corrections can produce deviations from its result.