AME2020 lists these atomic mass excesses for calcium ( )

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear constituents, size and binding · The nuclear force and nuclear models

The Nucleus Resolved, Ch How big a nucleus is, and what the mass surface knows

Problem

AME2020 lists these atomic mass excesses for calcium (

Z = 20

), in MeV:

^{44}\mathrm{Ca}

-41.469

^{46}\mathrm{Ca}

-43.140

^{47}\mathrm{Ca}

-42.345

^{48}\mathrm{Ca}

-44.225

^{49}\mathrm{Ca}

-41.300

^{50}\mathrm{Ca}

-39.589

. The neutron's mass excess is

8.071\,\mathrm{MeV}

. ((a)) Find

S_n

for

^{48}\mathrm{Ca}

and

^{49}\mathrm{Ca}

. ((b)) Find

S_{2n}

for

^{46}\mathrm{Ca}

^{48}\mathrm{Ca}

and

^{50}\mathrm{Ca}

, and the average fall of

S_{2n}

per neutron from

N = 26

28

and from

N = 28

30

. At which neutron number is there a step? ((c)) Find the odd-even staggering

\Delta_n

^{48}\mathrm{Ca}

and compare it with the refitted formula's

a_P/\sqrt{A}

a_P = 12.51\,\mathrm{MeV}