Old and new quasi-magic numbers. Nuclear structure physics Eivind 1964 to Eivind at 70 Igal Talmi The Weizmann Institute of Science Rehovot, Israel. Welcome.
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Nuclear structure physics
to Eivind at 70
The Weizmann Institute of Science
SIMPLICITY ARISES FROM THE COMPLEXITY.
This was realized almost 50 years ago.
Such changes occur all over the nuclear landscape.
in 38Cl: one 1d3/2 proton and a 1f7/2 neutron
in 40K: (1d3/2)3Jp=3/2 proton configuration and
is in good agreement with some experimental data.
In magic nuclei, energies of first excited
states are rather high as in 36S (Z=16, N=20)
where the first excited state is at 3.3 MeV,
considerably higher than in its neighbors.
Shell closure may be concluded if
valence nucleons occupy higher orbits
like 1d3/2 protons in the 38Cl, 40K case.
Shell closure may be demonstrated by
a large drop in separation energies (no
stronger binding of the closed shells!)
in J=0 states.
The other T=1 interactions are weak and
repulsive on the average.
It leads to a seniority type spectrum.
neutrons, is strong and attractive
on the average.
It breaks seniority in a major way.
by the attractive proton-neutron interaction
which determines its depth and its shape.
by the occupation numbers of neutrons and vice
versa. Thus, also shell closures depend on occupation numbers.
and in more detail in a review article in 1962.
The next example shows how such considerations may be applied.
two 1p3/2 protons?
interaction with a 2s1/2 neutron, hence, the
latter’s orbit may become lower in 11Be.
exact shell model calculation in a rather limited space.
be said that here the neutron number 8 is no longer a magic number.
measurement. It is rather small and yet, we used matrix elements
which were determined from stable nuclei.
appreciably extended and 11Be should be a “halo nucleus”.
It is amusing to see that similar arguments are presented as new
ones in 2001, 40 years later.
magic number N=20.
sufficiently higher than s and d orbits and N=20 seems to
affects more the s and d neutron orbits than the f orbit.
Thus, the neutron configuration is no longer the closed s,d shell
but has appreciable admixtures of 1f7/2 neutrons. In such nuclei,
N=20 is no longer a magic number.
should occupy the 1f7/2 shell.
indicating effects of interactions with higher configurations.
Ground states, far from perturbing states, have energies,
as well as neutron separation energies, which agree
very well with predictions of the seniority scheme for a
agreement with experimental data.
the proton quasi-magic number Z=40 disappears for neutron numbers higher than N=98.
Still, the first excited state in 22O is at 3.27 MeV.
two neutron separation
energies show a big
drop beyond 22O. It can
be said that
for Z=8, N=14 is a
(unlike N=64 for Z=50). The drop in proton separation energies beyond Z=64 is rather small.
SIMPLICITY OUT OF THE COMPLEXITY
of their calculations.
and j’ orbits involved. As a result, when a certain proton shell is being filled, the relative positions of single neutron orbits may change considerably.”
pure (7/2)n configurations.
of particle number n.
in seniority for j=7/2.
wave functions of magic nuclei are well determined. So are states with one valence nucleon or hole in such nuclei.
the 1f7/2 orbit, not all states are pure but binding energies
follow the predictions of the seniority scheme. Also excited
states show features of a (7/2)n configurations.
Due to properties of the T=0 interactions, this would not be
so had the 28 neutrons not formed a closed shell.
It is amazing that even for Z=14, N=28 is a magic number
as demonstrated by the existence of a bound 42Si nucleus.