__KING FAHD UNIVERSITY OF PETROLEUM & MINERALS__

**DEPARTMENT OF PHYSICS**

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**PHYS 422 Nuclear and Particle Physics (3-0-3)**

**Second Semester 2004 (032)**

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__Homework # 2 __

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**HW2#P1: **

For a nucleus show that the electric quadrupole moment is

Show that If
is concentrated along the z-axis Q ~ + 2

**HW2#P2:
**

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A nuclear charge distribution more
realistic than the uniformly charged distribution is the Fermi distribution
.

(a)
Sketch this
distribution and compare with Figure 3.4.

(b)
Find the value
of a if t = 2.3 fm/

(c)
What is the
significance of the parameter R?

(d)
Evaluate (r^{2})
according to this distribution.

**HW2#P3:
**Krane 3.7

(a)
From the known
masses of ^{15}O and ^{15}N, compute the difference in binding
energy.

(b)
Assuming this
difference to arise from the difference in Coulomb energy, compute the nuclear
radius of ^{15}O and ^{15}N.

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HW2#P4: **
Krane 3.10

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**
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For each of the following nuclei use
the semiempirical mass formula to compute the total binding energy and the
Coulomb energy: (a) ^{21}Ne; (b) ^{57}Fe; (c) ^{209}Bi;
(d) ^{256}Fm.

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HW2#P5: **
Krane 3.17

The spin-parity of ^{9}Be and ^{9}B are both
. Assuming in both cases that the spin and parity are
characteristic only of the odd nucleon, show how it is possible to obtain the
observed spin-parity of ^{10}B (3^{+}).
What other spin-parity combinations could also appear? (These are observed as
excited states of ^{10}B.)