Problems and Solutions on Thermodynamics and Statistical Mechanics

Statistical Phyaca 281

4s

3

The volume of the nucleus is given by V = -RiA, Ro M 1.4 x

Please give the result in MeV.

cm.

(Chicago)

Solution:

In the momentum space,

4v

h3

dn = -4n-p2dp,

where n is the number density of neutrons.

The total number of neutrons is

A = 1 dn = 16n-V LPF $dP

where PF is the Fermi momentum.

The total kinetic energy of the neutrons is

Hence ,

The volume V can be expressed in two ways:

4n 3(2~)~ -3 h

V = -R3A = - pF A, (putting h z - = 1)

3O 16n 27r

giving p~ = R,' (2) 'I3, and