Measurement of the γ emission probability of 173Yb using surrogate reactions

We performed the 174Yb(p,d) reaction in order to measure the gamma-emission probability of 173Yb. The identification of the ejectiles — allowing us to tag the production of 173Yb nuclei — was performed using the STARLiTeR detector system. Unusually, the “statistical“ γ-rays were used to determined the gammaemission probability and a spin distribution was extracted from it. A comparison with the spin distribution from the 174Yb(3He,α) reaction shows that the transferred angular momentum is similar in both reactions. 1 The surrogate reaction method Radiative neutron capture cross section measurements on stable nuclei are performed using a rather well mastered technique. However, it is much less straightforward when these cross section measurements are performed on radioactive nuclei. Such measurements being very challenging and even impossible to do, the surrogate reaction method, initially introduced by Cramer and Britt in 1970 [3], is used to obtain some informations about these unstable nuclei. The surrogate reaction method is based on the hypothesis that the decay of a compound nucleus is independent from its formation. Thus, the principle is to use a different target (stable or less radioactive) coupled to a suitable beam in order to produce the same compound nucleus whose the decay is then studied as illustrated by the Eq. 1. n + X → Z∗ a + Y → Z∗ + b (1) In Hauser-Feshbach theory [4], the radiative neutron capture cross section σA−1 (n,γ) can be related to the compound nucleus formation cross section σ(En, J, π) and to the decay branching ratio of the compound nucleus GA γ (E∗, J, π) via the following equation (the width fluctuation correlations between entrance and exit channels are neglected) [5]


The surrogate reaction method
Radiative neutron capture cross section measurements on stable nuclei are performed using a rather well mastered technique. However, it is much less straightforward when these cross section measurements are performed on radioactive nuclei. Such measurements being very challenging and even impossible to do, the surrogate reaction method, initially introduced by Cramer and Britt in 1970 [3], is used to obtain some informations about these unstable nuclei.
The surrogate reaction method is based on the hypothesis that the decay of a compound nucleus is independent from its formation. Thus, the principle is to use a different target (stable or less radioactive) coupled to a suitable beam in order to produce the same compound nucleus whose the decay is then studied as illustrated by the Eq. 1.
In Hauser-Feshbach theory [4], the radiative neutron capture cross section σ A−1 (n,γ) can be related to the compound nucleus formation cross section σ A (E n , J, π) and to the decay branching ratio of the compound nucleus G A γ (E * , J, π) via the following equation (the width fluctuation correlations between entrance and exit channels are neglected) [5] where J and π are the spin and the parity respectively. E n and E * are the kinetic energy of the incident neutron and the excitation energy of the compound nucleus respectively. Both quantities are linked together through the a e-mail: olivier.delaune@cea.fr Eq. 3 where M CN is the mass of the compound nucleus and S CN n its neutron separation energy. The compound nucleus formation cross section is usually determined from optical model calculation whilst the branching ratio G A γ is measured. Experimentally, one measures the decay probability P γ . It is related to the branching ratio via the relation where F A (E * , J, π) represents the probability that the compound nucleus is produced in the state J π with an excitation energy E * . Usually, the surrogate reaction method is used within the Weisskopf-Ewing limit [6] which stipulates that the branching ratio for the decay of the compound nucleus does not rely on the spin and the parity of the compound nucleus but only on its excitation energy. Thus, Eq. 2 becomes and G A γ (E * ) = P γ (E * ). Applied with some success to study the fission [1,2], the validity of the surrogate reaction method is undergoing on the nuclei from the rare earth region. Some works have shown that the transferred angular momentum in a (p,d) on rare-earth nuclei is around 5 [7]. This value is similar to the one found in ( 3 He,α) reactions implying also rare-earth nuclei [8]. Both values are much higher than the angular momentum transferred in a neutron-induced reaction. The comparison is not direct since the compound nuclei are not the same. Here, we want to perform a direct comparison, i.e. involving the same compound nucleus. Thus, we  [9]. The radiative capture cross section extracted from this surrogate reaction was about 10 times larger than the cross section measured with a neutron beam [10] due to the higher transferred angular momentum. In both experiments, we used the same experimental technique that uses the "statistical γ-rays" and that will be described in the Sec. 2.2.

Experimental setup
A schematic view of the experimental setup is shown in Fig. 1. A proton beam was accelerated at 25 MeV (∼ 2-enA) within the K150 superconducting cyclotron in the Cyclotron Institute at Texas A&M University. It impinged on a 600 μg/cm 2 thick self-supporting 174 Yb target. The 173 Yb nuclei are produced via the reaction 174 Yb(p,dγ) 173 Yb, used as the surrogate reaction for the 172 Yb(n,γ) reaction. The deuterons were collected and identified using the STARS setup (Silicon Telescope Array for Reaction Studies) [11] allowing to determine that 173 Yb nuclei were produced. The STARS setup was composed of one ΔE-E telescope located forwards from the target. It was composed of two annular silicon detectors highly segmented allowing to measure both the polar angle θ and the azimuthal angle ϕ. The telescope covers angles ranging from 40 • to 65 • .
The ΔE detector was 150 μm thick while the E one is 1007 μm thick. An aluminium foil, 200 μg/cm 2 thick, was placed in front of each telescope in order to remove the δ electrons coming from the target.
To detect γ-rays in coincidence with deuterons, we used the LIBERACE setup (Livermore-Berkeley Array for Collaborative Experiments) [11]. It is composed of 6 clovers of high purity germanium detectors coupled to bismuth germanate oxide (BGO) crystal in order to remove the events coming from Compton diffusion.
A full description of the experimental setup is given in the Ref. [11].

Gamma emission probability
The gamma emission probability is defined as where N γ−d is the number of coincidences between a γ-ray and a deuteron, N d is the number of single deuterons and represents the probability to detect a γ cascade. Experimentally, N d is determined when a particle passes through the ΔE and the E detectors and is identified as a deuteron, and N γ−d (E * ) corresponds to the number of events where a deuteron is detected in coincidence with any γ-ray as proposed by Boutoux et al. [12].

Analysis
The two silicon detectors (ΔE-E of the telescope) were calibrated using a 226 Ra α source. The resolution (FWHM) is typically of 52 keV for the ΔE detector and of 45 keV for the E one at 7690 MeV.
Then, the total kinetic energy of the deuterons, T e , is obtained using the Eq. 7 T e = ΔE + E + δE non-measured (7) where • ΔE is the energy deposited in the ΔE detector; the energy is collected from the rings because of the better energy resolution compared to the one obtained from the sectors. In the case where two rings are hit, if they are adjacent, both energies are summed; • E is the energy deposited in the E detector; it is coming from the sectors; • δE non-measured corresponds to the non-measured energy losses; they are estimated using the SRIM software.
From the polar angle of the ejectile, θ e , given by the ring which is hit and the total kinetic energy of the ejectile, T e , the excitation energy E * of the recoil nucleus can be determined via the Eq. 8 where Q is the Q-value of the reaction, T is the total kinetic energy and M the mass. The indices b, e and r correspond respectively to the beam, the ejectile and the recoil nucleus. A two-body reaction is assumed to establish this relation as well as the fact that the excitation energy of the system is fully transferred to the recoil nucleus. Usually, the N γ−d value is determined by tagging on a given γ-transition on which the γ-cascade terminates. It works quite well on the even-even nucleus but for other nuclei, the P γ may be biased if some cascades do not pass through this transition or if the level scheme is not known precisely.
E* (MeV) 5 5.  Figure 3. Gamma emission probability P γ as a function of the excitation energy E * .
To bypass these problems, we used the EXEM method. This method relies on the hypothesis that the variation of the γ-cascade detection efficiency below the neutron separation energy can be extrapolated above this energy. Below the neutron separation energy S n , the only way for the compound nucleus to release its excitation energy is to emit γ-rays. Thus, the gamma emission probability is equal to 1 and the γ-cascade detection efficiency is determined by (E * < S n ) = Above the neutron separation energy, γ-rays from the 174 Yb(p,dnγ) 172 Yb* channel may be detected. In order to suppress this contribution, a threshold in energy is applied. If the threshold is high enough, the γ-rays coming from the nucleus produced after the neutron evaporation will be removed as shown on Fig. 2.
The γ-emission probability has been fitted using a relation similar to the Eq. 4. The F A function is defined as The spin distribution is assumed to be described as a Gaussian distribution (J is the centroid of the Gaussian and σ corresponds to the standard deviation of the Gaussian) and to not depend on the excitation energy. In addition, both parities are assumed to be equiprobably populated. The other term from the Eq. 4, the branching ratio G γ , is given by the TALYS 1.2 code [13]. Some informations related to the technical aspects are given in the Ref. [14].
The result of the fit, shown on the Fig. 3, leads to a mean value ofJ = 3.68 ± 0.21 and to a standard deviation of σ = 4.06 ± 0.36 as parameters for the spin distribution. These values have to be compared to the ones got from the study of the 174 Yb( 3 He,α) 173 Yb reaction [9]: J = 3.87 ± 0.21 and σ = 3.22 ± 0.21 . Both spin distributions are rather similar. This can be interpreted as the fact the angular momenta transferred by the (p,d) and the ( 3 He,α) reactions are quite similar confirming the findings from a previous work where a comparison of the transferred angular momenta was done among different systems and reactions [7].