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J. E. Escher et al.
and inelastic breakup, breakup followed by partial fusion (of either the neutron
or proton), and complete fusion followed by evaporation are known contribute to
inclusive (d,p) measurements. Inclusive (d,p) reactions were already discussed in the
1970s, but disagreements about the proper theoretical formalism persisted [24–26].
Recently, several groups revisited the problem [27–29] and developed a consistent
formalism [30]. The numerical implementation of Ref. [27] was subsequently used
to calculate the spin-parity distribution relevant to a recent 95 Mo(d,pγ ) surrogate
measurement. Modeling the decay of 96 Mo ∗ made it then possible to indirectly
determine the 95 Mo(n,γ ) cross section, which was found to be in excellent agreement with the known capture cross section, thus providing a valuable benchmark
for future (d,p) surrogate reaction applications [13].
2.3 Capture Cross Sections from Inelastic Scattering Reactions
Inelastic scattering is potentially a very valuable surrogate reaction mechanism [7,
16] that can also be used in inverse-kinematics experiments at radioactive-beam
facilities. In the past, inelastic scattering with charged particles has been used
extensively to study giant resonances. These studies demonstrate that inelastic
scattering produces compound nuclei up to very high excitation energy (10s
of MeV). Thus, it becomes possible to observe γ emission, neutron emission,
and two consecutive neutron emission events in one experiment. This makes it,
in principle, possible to determine (n,γ ), (n,n’), and (n,2n) cross sections from
surrogate inelastic scattering experiments. A proper theoretical description of such
experiments requires the integration of nuclear structure and reaction descriptions,
along the lines of the developments carried out in Refs. [31–35].
3 Outlook
Indirect methods are critical for determining cross sections for reactions on unstable
isotopes. The approach outlined here is, in principle, applicable to other decay channels (and to other entrance channels). When considering other entrance channels, the
projectile-target fusion calculation has to be modified accordingly. For example, to
determine a (p,γ ) cross section, a proton-nucleus optical model potential has to be
employed to calculate the compound nucleus formation in the desired reaction. The
decay models can be constrained analogously to the (n,γ ) case. When other exit
channels are of interest, different coincidence probabilities have to be measured.
For fission, one can detect fission fragments in coincidence with the outgoing
particle from the surrogate reaction [1]. For neutron or charged-particle channels,
it is possible to detect the emitted particle of interest or—in analogy to the case
discussed in Sect. 2—a γ transition that is characteristic of the channel of interest.
J. E. Escher et al.
and inelastic breakup, breakup followed by partial fusion (of either the neutron
or proton), and complete fusion followed by evaporation are known contribute to
inclusive (d,p) measurements. Inclusive (d,p) reactions were already discussed in the
1970s, but disagreements about the proper theoretical formalism persisted [24–26].
Recently, several groups revisited the problem [27–29] and developed a consistent
formalism [30]. The numerical implementation of Ref. [27] was subsequently used
to calculate the spin-parity distribution relevant to a recent 95 Mo(d,pγ ) surrogate
measurement. Modeling the decay of 96 Mo ∗ made it then possible to indirectly
determine the 95 Mo(n,γ ) cross section, which was found to be in excellent agreement with the known capture cross section, thus providing a valuable benchmark
for future (d,p) surrogate reaction applications [13].
2.3 Capture Cross Sections from Inelastic Scattering Reactions
Inelastic scattering is potentially a very valuable surrogate reaction mechanism [7,
16] that can also be used in inverse-kinematics experiments at radioactive-beam
facilities. In the past, inelastic scattering with charged particles has been used
extensively to study giant resonances. These studies demonstrate that inelastic
scattering produces compound nuclei up to very high excitation energy (10s
of MeV). Thus, it becomes possible to observe γ emission, neutron emission,
and two consecutive neutron emission events in one experiment. This makes it,
in principle, possible to determine (n,γ ), (n,n’), and (n,2n) cross sections from
surrogate inelastic scattering experiments. A proper theoretical description of such
experiments requires the integration of nuclear structure and reaction descriptions,
along the lines of the developments carried out in Refs. [31–35].
3 Outlook
Indirect methods are critical for determining cross sections for reactions on unstable
isotopes. The approach outlined here is, in principle, applicable to other decay channels (and to other entrance channels). When considering other entrance channels, the
projectile-target fusion calculation has to be modified accordingly. For example, to
determine a (p,γ ) cross section, a proton-nucleus optical model potential has to be
employed to calculate the compound nucleus formation in the desired reaction. The
decay models can be constrained analogously to the (n,γ ) case. When other exit
channels are of interest, different coincidence probabilities have to be measured.
For fission, one can detect fission fragments in coincidence with the outgoing
particle from the surrogate reaction [1]. For neutron or charged-particle channels,
it is possible to detect the emitted particle of interest or—in analogy to the case
discussed in Sect. 2—a γ transition that is characteristic of the channel of interest.