Surrogate Reactions Approach
223
channel of interest in current surrogate experiments are expected to be negligible,
so no correction factor is included in Eq. 1.
This idea was discussed in Refs. [1, 11] and recently used to determine the
neutron capture cross sections for 87 Y and 90 Zr from surrogate (p,dγ ) data [12]
and 95 Mo from surrogate (d,pγ ) data [13]. The 87 Y(n,γ ) result represents the first
application of this method to an unstable isotope ( 87 Y has a half-life of 79.8 h and
prior cross section calculations had to rely on regional systematics). The 90 Zr(n,γ )
and 95 Mo(n,γ ) results, on the other hand, serve as benchmarks of the approach.
This approach presupposes that the spin-parity distributions F δ (E ex , J, π) can
be calculated for the surrogate reaction selected. This is non-trivial, as the CN
excitation energies relevant to capture are typically on the order of 5–10 MeV, where
standard direct-reaction descriptions, such as DWBA, are no longer valid. Here, we
discuss the theory developments required to determine the capture cross sections.
2.1 Capture Cross Sections from (p,d) Pickup Reactions
In Ref. [12], the (p,d) reaction was used to produce the compound nuclei 88 Y ∗ and
91 Zr ∗ , which are relevant to determining the 87 Y(n,γ ) and 90 Zr(n,γ ) cross sections,
respectively. Natural 89 Y and enriched 92 Zr targets were bombarded by a 28.5MeV proton beam, produced by the K150 Cyclotron at Texas A&M University. The
energy and angular distributions of the outgoing deuterons were measured using the
Silicon Telescope Array for Reaction Studies (STARS) [14]. The coincident γ rays
were detected with five HPGe clover detectors in the Livermore-Texas-Richmond
(LiTeR) array [7, 14]. The Surrogate coincidence probability P δγ (E ex ) was obtained
by measuring N δ , the total number of detected deuterons, and N δγ , the number
of coincidences between a deuteron and the γ -ray that identifies the relevant exit
channel: P
exp
δγ (E ex , θ d ) = N δγ (E ex , θ d )/N δ (E ex , θ d ))(E γ ), where γ ) denotes
the efficiency for detecting the exit channel γ -ray [15–17] (Fig. 1).
To calculate the surrogate spin-parity distribution F CN
δ (E ex , J, π) for the compound nucleus, the one-neutron removal reaction (p,d) has to be described. This
requires a reaction formulation as well as nuclear structure information. In the
90 Zr(n,γ ) example considered here, the surrogate reaction produces 91 Zr ∗ by
removing neutrons from inner shells of the 92 Zr nucleus: deep hole states are
involved in the production of 91 Zr ∗ near S n . Their location and fragmentation
as a function of E ex was obtained using the dispersive optical model approach
of Mahaux and Sartor [18]. At the high excitation energies involved, one-step
(p,d) pickup processes have to be complemented by contributions from two-step
processes such as (p,p’)(p’,d) and (p,d’)(d’,d), in which the initial 92 Zr or the final
91 Zr are inelastically excited. Due to the large number of states in the energy band
populated, the different contributions can be assumed to add incoherently. Angleintegrated (p,d) cross sections can be calculated and compared to measured (p,d)
cross sections as a cross-check for the calculations. While (p,d) reactions that
populate low-energy states with dominant single-particle character result in cross
223
channel of interest in current surrogate experiments are expected to be negligible,
so no correction factor is included in Eq. 1.
This idea was discussed in Refs. [1, 11] and recently used to determine the
neutron capture cross sections for 87 Y and 90 Zr from surrogate (p,dγ ) data [12]
and 95 Mo from surrogate (d,pγ ) data [13]. The 87 Y(n,γ ) result represents the first
application of this method to an unstable isotope ( 87 Y has a half-life of 79.8 h and
prior cross section calculations had to rely on regional systematics). The 90 Zr(n,γ )
and 95 Mo(n,γ ) results, on the other hand, serve as benchmarks of the approach.
This approach presupposes that the spin-parity distributions F δ (E ex , J, π) can
be calculated for the surrogate reaction selected. This is non-trivial, as the CN
excitation energies relevant to capture are typically on the order of 5–10 MeV, where
standard direct-reaction descriptions, such as DWBA, are no longer valid. Here, we
discuss the theory developments required to determine the capture cross sections.
2.1 Capture Cross Sections from (p,d) Pickup Reactions
In Ref. [12], the (p,d) reaction was used to produce the compound nuclei 88 Y ∗ and
91 Zr ∗ , which are relevant to determining the 87 Y(n,γ ) and 90 Zr(n,γ ) cross sections,
respectively. Natural 89 Y and enriched 92 Zr targets were bombarded by a 28.5MeV proton beam, produced by the K150 Cyclotron at Texas A&M University. The
energy and angular distributions of the outgoing deuterons were measured using the
Silicon Telescope Array for Reaction Studies (STARS) [14]. The coincident γ rays
were detected with five HPGe clover detectors in the Livermore-Texas-Richmond
(LiTeR) array [7, 14]. The Surrogate coincidence probability P δγ (E ex ) was obtained
by measuring N δ , the total number of detected deuterons, and N δγ , the number
of coincidences between a deuteron and the γ -ray that identifies the relevant exit
channel: P
exp
δγ (E ex , θ d ) = N δγ (E ex , θ d )/N δ (E ex , θ d ))(E γ ), where γ ) denotes
the efficiency for detecting the exit channel γ -ray [15–17] (Fig. 1).
To calculate the surrogate spin-parity distribution F CN
δ (E ex , J, π) for the compound nucleus, the one-neutron removal reaction (p,d) has to be described. This
requires a reaction formulation as well as nuclear structure information. In the
90 Zr(n,γ ) example considered here, the surrogate reaction produces 91 Zr ∗ by
removing neutrons from inner shells of the 92 Zr nucleus: deep hole states are
involved in the production of 91 Zr ∗ near S n . Their location and fragmentation
as a function of E ex was obtained using the dispersive optical model approach
of Mahaux and Sartor [18]. At the high excitation energies involved, one-step
(p,d) pickup processes have to be complemented by contributions from two-step
processes such as (p,p’)(p’,d) and (p,d’)(d’,d), in which the initial 92 Zr or the final
91 Zr are inelastically excited. Due to the large number of states in the energy band
populated, the different contributions can be assumed to add incoherently. Angleintegrated (p,d) cross sections can be calculated and compared to measured (p,d)
cross sections as a cross-check for the calculations. While (p,d) reactions that
populate low-energy states with dominant single-particle character result in cross