Krane

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Krane
1p3/2 ? 1d5/2 leaves 1 odd particle in 1p3/2
orbital Jp 3/2- a1(1p3/2)3(1d5/2)2
a2(1p3/2)3(1d5/2)(2s1/2)
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Approximate Single-Particle Potentials
Spherical well V Harmonic
oscillator V Woods-Saxon V
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Prussin
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Prediction of ground state spin and parity
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Odd-Odd
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Schematic diagram of (d,p) reaction
Proton tends to travel in forward direction
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Proton angular distributions show
diffraction-like patterns due to interference
from reactions occurring on opposite sides of the
target nucleus
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Angular distributions of protons from 58Ni(d,p)
reaction populating different states in 59Ni
Cohen
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By determining L transfer in direct reactions, we
can deduce spin and parity values (or at least
ranges of spins) of states produced Simplest
example (d,p) reaction on an even-even
target Jp(target) 0 J(product) L
½ p(product) (-1)L ? transfer reactions
have played an important role in nuclear
spectroscopy.
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Consider 209Pb127
Shell model orbitals for N gt 82
Expect gs due to 2g9/2 and excited states
from 1i11/2, 1j15/2, 3d5/2, etc.
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Q3D magnetic spectrograph Useful for studying
transfer reactions
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Simple model of excited states
Model excited states as independent particles
moving in mean-field, but one or more particles
in a higher orbit particle-hole excitation
particle
hole
two-particle, two-hole (2p2h) excitation
one-particle, one-hole (1p1h) excitation
original configuration
7/2
3/2
more complicated
This works surprisingly well for some nuclei,
especially just outside a closed shell
9/2
3/2-
3/2
5/2-
5/2
7/2-
single-particle states
19O
43Ca
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Difference between actual binding energy and that
calculated using semi-empirical mass formula
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Energy of 1st excited state in even-A lead nuclei
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Solar-system abundances as a function of A
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gs(p) 5.585 gl(p) 1 gs(n) - 3.826 gl(n)
0
Krane
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Experimental values and shell-model estimates of
nuclear magnetic moments of odd-A nuclei
odd proton
odd neutron
Krane
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Krane
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Deformed nuclear shapes
Prolate spheroid Ellipse rotated about major
axis b gt 0 ground states of deformed nuclei
have b 0.3
Oblate spheroid Ellipse rotated about minor
axis b lt 0
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Prussin
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Prolate
Oblate
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Oblate
Prolate
Prussin
Krane
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Oblate
Prolate
Prussin
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Oblate
Prolate
Prussin