*
Received
on:
28/02/2021;
Accepted
on:
30/05/2021*

**Abstract: **
This
paper
provides
a study
of the
rotational
properties
of heavy
and
medium
nuclei,
particularly
the
paired
nuclei
existing
in the
rare-earth,
including
Gd, Er,
…, first
to have
a good
representation
of the
intrinsic
prolate
fundamentals
of the
considered
nuclei.
The most
important
residual
nuclear
interaction
is the
pairing
force
which
makes it
possible
to
couple
the
nucleons
in
pairs.
To take
it into
account,
we
introduce
the
Bardeen-Cooper-Shrie
formalism
(BCS),
developed
to
describe
the
phenomenon
of
superconductivity.
The test
wave
function
is then
more
elaborate
than
that of
Hartree-Fock
and
corresponds
to a
state no
longer
of
independent
particles,
but of
independent
quasi-particles.
A
quasi-particle
state (qp)
is a
linear
combination
of
particles
and
holes.
The
Routhian
Hartree-Fock
model
through
the
analysis
of the
experimental
spectra
of
rotation
of the
deformed
nucleus
was
usewd.
Knowing
that
this was
originally
expanded
by
Bohr-Mottelson
by
applying
I(I+1)
expansion,
we
modified
an
existing
fixed
code (HF)
with
axial
symmetry,
which
extended
in a way
that
allows
us to
add
constraints
on the
angular
momentum
and
kelvin
rotation
to the
Hamiltonian
known as
Cr.HF (cranking
version
of this
formalism),
initially
studied
by P.
Quentin.
This
modification
led to
good
results,
especially
the
spectra
of
rotation
and
the
angular
velocities
as a
function
of the
angular
momentum.
Besides,
it led
to a
decrease
in the
moment
of
inertia
after it
was
large in
some
models,
such as
in the
Hartree-Fock-Bogoliubov
(HFB)
model.
The
rotational
properties
and the
moments
of
inertia
of the
super-deformed
bands of
some
deformed
nuclei
have
been
studied
as well
as in
the mass
regions
A=190;
A=160.
The
results
were
compared
with
experimental
results
which
gave
good
agreement.
This
work
will
offer an
interesting
perspective
necessary
for
certain
improvements
or
extensions
of the
Cr.HF.

**
Keywords:**
Microscopic
mean
field,
Collective
nuclear
rotation,
Angular
momentum
Routhian
Hartree-Fock
(RHF)
model,
Inertia
moments,
Angular
velocity.

**
References
**

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