234
V. G. Gueorguiev et al.
deformation. Contributions from higher-order reaction mechanisms may need to be
considered [6] in the future.
In analogy with the rotor-plus-particle model [7], we view excited states in
156 Gd as rotational states built on intrinsic states consisting of a neutron hole in
the 157 Gd core; that is, a neutron removal from a deformed Woods–Saxon-type
single-particle state [8] in 157 Gd. To understand the impact of the deformation
and what should be considered as a small deformation, calculations of Woods–
Saxon-type single-particle states were performed using several codes [9–15]. For
small non-zero deformation, we used the codes from Ref. [10–13], while for large
deformation we selected only the code by Cwiok et al. [10]. The pairing effects
within the core are accounted for through the BCS pairing model [16, 17], while
the particle–core interaction usually dominated by a Coriolis coupling is accounted
for via first-order perturbation theory to the particle–core Coriolis coupling [17].
The spectroscopic factor associated with each state is the expansion coefficient of
the deformed neutron state in a spherical Sturmian basis along with the spherical
form factors [17]. The cross section for one-neutron transfers to each excited state
in 156 Gd is calculated as coherent contribution using a standard reaction code [15]
based on spherical basis states. The Sturmian basis is a collection of states that are
solutions to an equation that is almost the same as the Schödinger equation under
consideration, for fixed eigenenergy, but for a potential depth that is varied until
the boundary conditions are satisfied [18, 19]. Using such basis states comes at
the expense of a more complicated expansion but guarantees completeness and the
correct asymptotic tail of the wave function and often results in fast convergence
and small model spaces.
The resulting model calculations result in discrete energy states (see, e.g., Fig. 5
in Ref. [17]), and cross sections with sharp peaks (Fig. 9 in Ref. [17]), which
cannot be directly compared to experiments. The current description does not
include an explicit treatment of the couplings between the doorway states and
more complicated configurations, which result in the damping of these states into
the compound nucleus. We account for this damping by introducing a Lorentzian
distribution function, which smoothes out the cross section in energy [17].
Our calculations predict that, within the assumptions discussed here, the reaction
3 He+ 157 Gd → 4 He+ 156 Gd produces a well-behaved formation probability P(J π ,E)
within the energy range relevant to the desired reaction 155 Gd+n → 156 Gd . It is
observed that the centroid and shape of the Gaussian distributions of the positive and
negative parity states of the compound system can be significantly different from
each other (see Fig. 1). Thus, one has to carefully verify whether it is appropriate
to use the same Gaussian distribution for positive and negative parity states as has
been done in some surrogate reaction models [20].
V. G. Gueorguiev et al.
deformation. Contributions from higher-order reaction mechanisms may need to be
considered [6] in the future.
In analogy with the rotor-plus-particle model [7], we view excited states in
156 Gd as rotational states built on intrinsic states consisting of a neutron hole in
the 157 Gd core; that is, a neutron removal from a deformed Woods–Saxon-type
single-particle state [8] in 157 Gd. To understand the impact of the deformation
and what should be considered as a small deformation, calculations of Woods–
Saxon-type single-particle states were performed using several codes [9–15]. For
small non-zero deformation, we used the codes from Ref. [10–13], while for large
deformation we selected only the code by Cwiok et al. [10]. The pairing effects
within the core are accounted for through the BCS pairing model [16, 17], while
the particle–core interaction usually dominated by a Coriolis coupling is accounted
for via first-order perturbation theory to the particle–core Coriolis coupling [17].
The spectroscopic factor associated with each state is the expansion coefficient of
the deformed neutron state in a spherical Sturmian basis along with the spherical
form factors [17]. The cross section for one-neutron transfers to each excited state
in 156 Gd is calculated as coherent contribution using a standard reaction code [15]
based on spherical basis states. The Sturmian basis is a collection of states that are
solutions to an equation that is almost the same as the Schödinger equation under
consideration, for fixed eigenenergy, but for a potential depth that is varied until
the boundary conditions are satisfied [18, 19]. Using such basis states comes at
the expense of a more complicated expansion but guarantees completeness and the
correct asymptotic tail of the wave function and often results in fast convergence
and small model spaces.
The resulting model calculations result in discrete energy states (see, e.g., Fig. 5
in Ref. [17]), and cross sections with sharp peaks (Fig. 9 in Ref. [17]), which
cannot be directly compared to experiments. The current description does not
include an explicit treatment of the couplings between the doorway states and
more complicated configurations, which result in the damping of these states into
the compound nucleus. We account for this damping by introducing a Lorentzian
distribution function, which smoothes out the cross section in energy [17].
Our calculations predict that, within the assumptions discussed here, the reaction
3 He+ 157 Gd → 4 He+ 156 Gd produces a well-behaved formation probability P(J π ,E)
within the energy range relevant to the desired reaction 155 Gd+n → 156 Gd . It is
observed that the centroid and shape of the Gaussian distributions of the positive and
negative parity states of the compound system can be significantly different from
each other (see Fig. 1). Thus, one has to carefully verify whether it is appropriate
to use the same Gaussian distribution for positive and negative parity states as has
been done in some surrogate reaction models [20].