Dietrich, F S

ESCHER, J

Forssén, C

Gueorguiev, V G

Hoffman, R

Kelley, K

CERN Document Server

PoS(NIC-IX)224PoS(NIC-IX)224Compound-nuclear reaction cross sections viaSurrogate measurementsChristian Forssén∗ †, Frank S. Dietrich , Jutta Escher , Vesselin G. Gueorguiev,Robert D. Hoffman, and Kevin Kelley‡ §Lawrence Livermore National Laboratory, P.O. Box 808, L-414, Livermore, CA 94551, USAE-mail: c.forssen@fy.chalmers.seIndirect methods play an important role in the determination of nuclear reaction cross sections.Often the cross section needed for a particular application cannot be measured directly since therelevant energy region is inaccessible or the target is too short-lived. This is particularly truefor many reactions of interest to astrophysics. An innovative indirect approach to compound-nuclear reactions has recently been used to obtain cross sections for neutron-induced fission forvarious actinide targets via “Surrogate” reactions [1 – 5]. In the present paper we will discuss thefeasibility of using the Surrogate approach for neutron-capture reactions at low energies, relevantto the astrophysical s process. In particular, applications involving mass 90-100 nuclei will bediscussed.International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX25-30 June 2006CERN∗Speaker.†Present address: Fundamental Physics, Chalmers University of Technology, 412 96 Gothenburg, Sweden‡Present address: Department of Physics, Brigham Young University-Idaho, 525 South Center Street, Rexburg, ID83460, USA§This work was partly performed under the auspices of the U. S. Department of Energy by the University ofCalifornia, Lawrence Livermore National Laboratory, under contract No. W-7405-Eng-48. Support from the LDRDcontract No. 04–ERD–058, and from U.S. Department of Energy, Office of Science, (Work Proposal Number SCW0498)is acknowledged.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(NIC-IX)224PoS(NIC-IX)224Compound-nuclear reaction cross sections via Surrogate measurements Christian Forssén1. IntroductionCross sections for unstable nuclei are very difficult to measure, but they also play an importantrole for addressing some of the most compelling questions of basic science. Among the unansweredmysteries about the nature and evolution of our universe is the origin of the heavy elements [6].Much effort is currently being devoted to exploring nuclear processes, such as the s and r processes(“slow” and “rapid” neutron-capture processes), and astrophysical environments that can producethe elements between iron and uranium. Of particular interest in the context of the s process arebranch points, unstable nuclei that are produced in the s process with a life time long enough toallow the s process to proceed by either neutron capture or β decay [7]. A crucial ingredient fordetermining the probability of one path dominating over the other is the associated neutron-capturecross section. Calculated abundance patterns can be compared to data from stellar spectroscopy oranalyses from presolar dust grains. Such comparisons impose stringent tests on available s-processmodels, including the nuclear physics input, and provide valuable information on the physicalconditions under which the s process takes place. In addition, accurate and precise knowledge ofthe s process provides important constraints for the r process [8].Direct cross section measurements for neutron-capture reactions on branch-point nuclei aredifficult since they involve (by definition) unstable targets. Producing relevant isotopes for exper-iments in inverse kinematics will remain challenging for radioactive beam facilities. Moreover,cross section calculations are nontrivial since they require detailed knowledge of the nuclear struc-ture (level densities, gamma strengths functions, etc.) involved. In this contribution, we will discussan indirect method for determining cross sections for compound-nuclear reactions, the SurrogateNuclear Reactions method. The next section gives a brief outline of the Surrogate approach. Dif-ferent options for the utilization of experimental data from a Surrogate experiment are presented inSection 3, and the particular application of the method to neutron-capture reactions for astrophysicsis presented in Section 4. Some concluding remarks follow in Section 5.2. The Surrogate ApproachThe “Surrogate Nuclear Reactions” method, originally presented in [9, 10], combines exper-iment with theory to obtain cross sections for compound-nuclear reactions, a+A → B∗→ c+C,involving difficult-to-produce targets, A. In the Surrogate approach, B∗ is produced by means of analternative (“Surrogate”) reaction, e.g. d+D→ b+B∗, and the desired decay channel (B∗→ c+C)is observed in coincidence with the outgoing particle b. The reaction cross section is then obtainedby combining the calculated cross section for the formation of B∗ (from a+A) with the measureddecay probabilities for this state [5, 11].In the past, both inelastic scattering and transfer reactions have been employed to obtain Sur-rogate estimates for fission cross sections [4, 9, 10]. However, the present contribution focuseson (n,γ) reactions for spherical or near-spherical mass 90-100 targets. Many such reactions playan important role in the astrophysical s process. An example, that has been discussed recently inconnection to the question of the mixing efficiency in AGB stars [12], is 95Zr(n,γ)96Zr. It will notbe possible to measure the cross section for this reaction in the near future. However, a possible2PoS(NIC-IX)224PoS(NIC-IX)224Compound-nuclear reaction cross sections via Surrogate measurements Christian ForssénSurrogate reaction that could be used to populate the intermediate 96Zr state is 96Zr(α ,α ′)96Zr,which would allow for studying its subsequent gamma decay.In the Hauser-Feshbach formalism, the cross section for the “desired” reaction a+A→ B∗→c+C takes the form:σαχ(Eα) =∑J,piσCNα (Eex,J,pi) GCNχ (Eex,J,pi) , (2.1)with α denoting the entrance channel a+A and χ representing the relevant exit channel c+C. Theexcitation energy of the compound nucleus, Eex, is related to the center-of-mass energy Eα via theenergy needed for separating a from B: Eα = Eex−Sa(B). In many cases the formation cross sec-tion σCNα = σ(a+A→ B∗) can be calculated to a reasonable accuracy by using optical potentials,while the theoretical branching ratios GCNχ for the different channels χ are often quite uncertain.The objective of the Surrogate method is to determine or constrain these decay probabilities ex-perimentally. Under certain conditions, the branching ratios become approximately independent ofthe spin and parity of the decaying state. This limit is known as the Weisskopf-Ewing limit and isparticularly relevant for the analysis of Surrogate experiments as we will discuss below.The probability for forming B∗ in the Surrogate reaction (with energy Eex, angular momentumJ, and parity pi) is FCNδ (Eex,J,pi), where δ denotes the entrance channel d+D. We note that thepopulation of the compound nucleus following the desired and the Surrogate reactions can be verydifferent from each other. This is known as the J,pi population mismatch. However, it is thequantityPδ χ(Eex) =∑J,piFCNδ (Eex,J,pi) GCNχ (Eex,J,pi) , (2.2)which gives the probability that the compound nucleus B∗ was formed at an energy Eex and de-cayed into channel χ , that can be obtained experimentally. This is the information that should becombined with theory to extract the desired cross section σαχ(Eα)..3. Theoretical analysis using decay data from a Surrogate experimentThe decay data from a Surrogate experiment can be utilized in several ways. Let us brieflydiscuss three different approaches:1. Assuming that the Weisskopf-Ewing limit is valid for all energies and that consequently theJ,pi population mismatch is irrelevant.2. Using direct reaction theory, possibly in combination with experimental signatures, to modelthe J,pi distribution following the Surrogate reaction.3. Normalizing calculated branching ratios to the measured decay probabilities in an energyregion for which the Weisskopf-Ewing limit is valid.Note that the first approach will give you the desired cross section directly from the measureddecay probability with the single theoretical input being the formation cross section σCNα (Eex).This approach was used in the original version of the method [9, 10], and is still being used forsome applications [3]. It is also implicit in approximations to the full Surrogate formalism suchas the Ratio Method [4, 5]. However, it relies heavily on the applicability of the Weisskopf-Ewing3PoS(NIC-IX)224PoS(NIC-IX)224Compound-nuclear reaction cross sections via Surrogate measurements Christian Forssén0 1 2 3 4 5En [MeV]10-310-210-1100γ decay probability(n,γ)0-1-2-3-4-Negative parities0 1 2 3 4 5En [MeV]10-310-210-1100γ decay probability(n,γ)0+1+2+3+4+Positive paritiesFigure 1: Gamma decay probabilities of 92Zr∗ as a function of J,pi and equivalent neutron energy En. Thetotal gamma decay probability following neutron absorption is also shown.limit and can not be used, e.g., for low-energy neutron capture as will be seen in the discussion ofFig. 1.The latter two approaches require more theoretical input since a statistical reaction calculationmust be performed; and the experimental data is used to constrain the associated nuclear models. Inapproach (2) the direct-reaction probabilities FCNδ (Eex,J,pi) have to be determined theoretically, sothat the branching ratios GCNχ (Eex,J,pi) can be extracted from the measurements. These branchingratios are then inserted in Eq. (2.1) to yield the desired cross section. This procedure requiresa reliable theory for the population of continuum states in direct reactions, and their subsequentdamping into equilibrated compound nuclear states. Efforts to develop such a theory are underway,and the first attempts at employing this approach have already been performed [1, 2]. We note thatsupplemental experimental information such as measurements at several ejectile angles, gammamultiplicities, and individual gamma intensities are very useful to check the predicted populations.In applications where the decay probabilities are very sensitive to the J,pi population onecan try to exploit the fact that Surrogate experiments can give decay probabilities over a verywide energy range. By studying an energy region in which the Weisskopf-Ewing limit is valid,one can normalize calculated branching ratios to the measured decay probabilities. The deducednormalization factor can subsequently be used in the statistical reaction calculation of the crosssection in the desired energy range. As we will discuss next, this seems to be the method of choicefor extracting low-energy (n,γ) cross sections for spherical or near-spherical targets.4. Surrogate approach to neutron-capture reactionsThe gamma decay probabilities of compound-nuclear states just above the neutron separationthreshold can be very sensitive to the J,pi of the decaying state. The reason is the small number ofopen decay channels, usually not more than one or a few neutron channels plus the gamma channel,and the fact that the neutron transmission coefficients will be very large for s wave, and possibly pwave, channels while they are small for all other channels. This is clearly demonstrated in Fig. 1,which shows the gamma decay probabilities of 92Zr∗ compound-nuclear states as a function of their4PoS(NIC-IX)224PoS(NIC-IX)224Compound-nuclear reaction cross sections via Surrogate measurements Christian ForssénJ,pi and the equivalent neutron energy En = Eex−Sn. These results are obtained from a statisticalreaction calculation with nuclear model parameters from recently developed regional systematicsfor nuclei spanning the range 34 ≤ Z ≤ 46 [13]. It is clear from studying Fig. 1 that we are farfrom the Weisskopf-Ewing limit at small energies. Approach (1) outlined above can therefore notbe used. In addition, the sensitivity to the J,pi population is so strong that approach (2) would beextremely difficult to apply with good accuracy since it would require a very precise predictionof the J,pi population mismatch. Instead, approach (3) seems to be the best choice for extractinglow-energy neutron capture cross sections from Surrogate experiments. In the case shown here, theWeisskopf-Ewing limit sets in at around En ≥ 2.5 MeV, and experimental data at high energiescould therefore be used for a normalization of the decay model. We note that neutron capture crosssections modeled with the Hauser-Feshbach formula are most sensitive to the photon transmissioncoefficients and nuclear level densities. Preliminary simulations of this approach show that thenormalization of the decay model at high energies result in a very accurate, and almost modelindependent, prediction at the relevant low energies [14].5. Summary and outlookIn this paper we have discussed different options for utilizing decay data from Surrogateexperiments. Our main focus has been on the particular application of the method to extractlow-energy neutron capture cross sections for spherical or near-spherical targets. This turns out tobe a particularly difficult application, but the idea outlined in this presentation is very promising.More detailed studies will require further simulations and benchmark experiments.References[1] W. Younes and H. C. Britt, Phys. Rev. C 67, 024610 (2003).[2] W. Younes and H. C. Britt, Phys. Rev. C 68, 034610 (2003).[3] M. Petit et al., Nucl. Phys. A 735, 345 (2004).[4] J. T. Burke et al., Phys. Rev. C 73, 054604 (2006).[5] J. E. Escher and F. S. Dietrich, Determining (n, f ) cross sections for actinide nuclei indirectly: Anexamination of the Surrogate Ratio Method, submitted to Phys. Rev. C.[6] Committee on the Physics of the Universe, National Research Council, Connecting Quarks with theCosmos: Eleven Science Questions for the New Century, The National Academies Press, 2003.[7] F. Käppeler, Prog. Part. Nucl. Phys. 43, 419 (1999).[8] Y. Z. Qian, Prog. Part. Nucl. Phys. 50, 153 (2003).[9] J. D. Cramer and H. C. Britt, Nucl. Sci. Eng. 41, 177 (1970).[10] H. C. Britt and J. B. Wilhelmy, Nucl. Sci. Eng. 72, 222 (1979).[11] C. Forssén et al., Nucl. Phys. A 758, 130 (2005).[12] F. Herwig, N. Langer, and M. Lugaro, Astrophy. J. 593, 1056 (2003).[13] R. D. Hoffman, K. Kelley, F. S. Dietrich, R. Bauer, and M. G. Mustafa, Technical report, LawrenceLivermore National Laboratory, UCRL-TR-222275, 2006.[14] C. Forssén et al., Determining neutron-capture cross sections via the Surrogate Technique,manuscript in preparation.5

Compound-nuclear reaction cross sections via Surrogate measurements

Abstract

Similar works

Full text

Available Versions

CERN Document Server