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NUCLEAR STRIPPING REACTIONS1,2 By NORMAN K. GLENDENNING Lawrence Radiation Laboratory, University of California, Berkeley, California CONTENTS 1. INTRODUCTION...................................................... 191 2. SINGLE-NuCLEON STRIPPING REACTIONS. . . . .. . . . . . . . . . . . . . ... . . . .. 193 2.1 General form of the cross section.... .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 193 2.2 A ntisymmetrization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 196 2.3 Plane-wave calculation-Butler formula. .. . . . . . . . . . . . . . . . . . . . . . . .. 197 2.4 Distorted-wave method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 206 2.5 Distorting potential in stripping reactions. . . . . . . . . . . . . . . . . . . . . . . . .. 212 2.6 Some examples of distorted-wave calculations.... . . . . . . . . . . . . . . . . . .. 215 2.7 Nuclear structure and spectroscopic factors. . . . . . . . . . . . . . . . . . . . . . . .. 216 2.8 Polarization and angular correlation ............................. , 2 2 9 2.9 Rearrangement stripping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2 3 7 3. SINGLE-NuCLEON TRANSFER REACTIONS OTHER THAN (d, P). . . . . . . . . . . .. . 239 4. Two-NUCLEON TRANSFER REACTIONS................................... 2 40 4.1 General features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 240 4.2 Interpretation of some experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2 50 ApPENDIX. . . . . n n n n + . + 253 1. INTRODUCTION The transmutation of elements by bombardment with slow deuterons, followed by the emission of protons, and the interpretation of the reaction as a stripping process date from 1935. Oppenheimer & Phillips (138) explained the experimental results of Lawrence, McMillan & Thornton (113) in terms of the penetration of the neutron into the target nucleus while the proton remaned outside, beyond the Coulomb barrier. In these experiments the cross section was found to increase less rapidly over the energy region measured (up to 3.6 MeV) than was anticipated from the Gamow penetration factor for transmission of a charged particle through the Coulomb barrier of the nucleus. The physical picture treated shows a deuteron moving in the feld of the nucleus, being stretched by the action of the Coulomb repulsion on the proton, while the neutron attracted by the i nteraction with the nucleus is captured. Because the deuteron binding energy is small, it is easily polarized, and the reaction can occur without the proton having to enter the Coulomb barrier. Hence the variation of the cross section with energy is quite diferent from that of reactions in which a charged particle must actually enter the nucleus. ^ The survey of literature for this review was concluded in early 1963. Written while the author was a visitor during 1962-63 at Centre d'Etudes Nucleires, Saclay, and Institut du Radium, Orsay, France. The author expresses his appreciation to Professors C. Block and M. Jean for the opportunity of mHking that sojourn. 191 Annu. Rev. Nucl. Sci. 1963.13:191-260. Downloaded from www.annualreviews.orgby National University of Singapore on 05/08/11. For personal use only.Quick links to online content FurtherANNUALREVIEWS192 GLENDENNING However, the importance of stripping reactions relevant to the study of nuclear states was not rfcognized until at higher energies the angular distributions of resolved groups of protons corresponding to particular energy levels of the residual nucleus were measured (30, 93) . These angular distributions exhibit a pronounced structure at forward angles, which Butler recognized as implying the importance of high angular momenta (14, 31, 32, 33) . Since high angular momenta must correspond to large impact parameters, he concluded that the reactions proceed, at least in part, by a stripping process in which one of the particles of the deuteron is absorbed into the nucleus, while the other merely carries of the balance of energy and momentum. Moreover, since the reaction connects the ground state of the target to a specifc fnal state, the stripped particle can have carried into the nucleus only such angular momentum and parity as are consistent with their conservation. Their subtraction from the incident wave is refected in the angular distribution of the outgoing protons. That a connection exists between the angular distribution of the outgoing proton and the angular momentum of the state into which the neutron is stripped can be understood in the light of the following classical argument (36, 100). Let the momenta of the incident deuteron, the outgoing proton, and the stripped neutron be lkd, lkp, and lq, respectively. Energy conservation specifes the magnitude of kp, and momentum conservation requires that q=kd-kp' If the neutron is stripped into a state of orbital angular momentum ll and if we suppose that the deuteron is broken up at the point R, then 1 equals R Xq. Consequently Ik-kI Rl 1. For 1 O this inequality can be satisfed only for scattering angles greater than some minimum value which depends on 1. In any case, because of the small deuteron binding, the deuteron is broken up preferentially with the proton moving in the forward direction. For single-nucleon transfer reactions the angular momentum 1 of the bound state, which accordi ng to the above argument can be deduced by a measurement of the angular distribution, is uniquely connected with the parity of the fnal nuclear state and determines within limits its spin, if the initial state is known. This establishes the importance of stripping reactions and their inverse, pickup reactions, as a means of studying the properties of nuclear energy levels, as emphasized by Butler, and as confrmed subsequently by the abundance of information emanating from stripping experiments. The stripping reaction is discussed in this review from the point of view of its usefulness as a probe of the structure of nuclear states. The foundations of the theory are not examined. However, some heuristic derivations of i mportant results are given. In Section 2, the (d, p) reaction is discussed in considerable detail because it is the most thoroughly studied reaction and it serves to illustrate many Annu. Rev. Nucl. Sci. 1963.13:191-260. Downloaded from www.annualreviews.orgby National University of Singapore on 05/08/11. For personal use only.NUCLEAR STRIPPING REACTIONS 193 points relevant to other direct reactions. This reaction by its nature populates and has been used to identify single-particle states in the fnal nucleus [cf. (41,42,43, 128, 163)]. The inverse reaction (p, d) can be used to study the hole-states [d. (41, 73)]; and these reactions, together with several other single-nucleon transfer reactions, are discussed briefy in Section 3. In Section 4, reactions involving the transfer of two nucleons are considered. These reactions make levels of two-particle or hole excitation accessible for study [d. ( 10, 79)]. The literature on stripping reactions is vast. I have not seen, let alone read, all that has been published on the subject. Undoubtedly much interesting work has been overlooked, and to the reader thus cheated I make my apologies. Other reviews which impinge upon the subject have been written by Huby ( 100), Horowitz (98), Butler (36) , Breit (27), Banerjee ( 1 1), French (61), Macfarlane & French ( 117), Tobocman (178), and Austern (8) . 2. SINGLE-NuCLEON STRIPPING REACTIONS 2. 1 General form of the cross section.-The angular distribution of outgoing particles from the (d, p) stripping reaction was frst obtained by Butler (31, 32, 33, 36). His method involves matching, at the nuclear boundary, the wave function for the system in the interior and exterior regions of the nucleus, found after certain simplifying assumptions are made. However, the method is lengthy and involved. Other authors soon gave alternative treatments of the reaction, which under the appropriate assumptions gave the same or similar results (7, 34, 40, 44, 45, 57, 58, 62, 64, 65, 74, 75, 94,95,99,173,174,184,185). In this section we shall develop the general form of the diferential cross section for single-particle stripping reactions and discuss the spectroscopic signifcance of the results. I n subsequent sections the several current forms of the theory will be discussed together with its application to the analysis of experiments. The exact transition matrix element for the (d, p) reaction can be written (d. 64) 2. where\ d is the exact-state vector for the system and has outgoing spherical waves of deuterons at infni ty; tP is the wave function for the fnal system comprising proton and residual nucleus (A + 1) with no interaction between these two parts; Vpn is the proton-neutron interaction and VpA is the protontarget interaction. Since the exact solution q d is not available, an approximate expression for T has to be found (see Appendix) : T(d. p),.. (p(-) I V = +(1 P) VpAP I xP 3. where P i

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