Deuteron Stripping Reactions Research Articles

Deuteron Stripping and Pickup Reactions in Oxygen-16

The reactions ${\mathrm{O}}^{16}(d, p){\mathrm{O}}^{17}$ and ${\mathrm{O}}^{16}(d, t){\mathrm{O}}^{15}$ were studied by bombarding thin nickel oxide foils with 15-Mev deuterons from the University of Pittsburgh cyclotron. The reaction particles were magnetically analyzed and detected either by nuclear emulsions or by a CsI(Tl) scintillator. Angular distributions and absolute cross sections were obtained for the first six states of ${\mathrm{O}}^{17}$ and for the ground state of ${\mathrm{O}}^{15}$. Reduced widths having values ${\ensuremath{\bigominus}}^{2}=0.045, 0.16, 0.0024, 0.0024, 0.0071, 0.047, \mathrm{and} 0.012$, respectively, were extracted from a comparison of the data with the predictions of Butler stripping theory. The most notable results of the ($d, p$) experiment indicate that: (1) the ${\frac{7}{2}}^{\ensuremath{-}}$ state at 3.846 Mev does not appear to be a good $1{f}_{\frac{7}{2}}$ single-particle state, (2) the $2{p}_{\frac{3}{2}}$ single-particle component seems to be fragmented over more than two states, and (3) the ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$ state at 3.058 Mev contains a $2{p}_{\frac{1}{2}}$ single-particle component. The results of the ($d, t$) experiment suggest a dependence of the $1p$ single-particle reduced width on $Q$ value.

Gamma Rays from Deuteron Stripping Reactions

The distorted-wave Bonn approximation is used to calculate the p- gamma angular correlation from several deuteron-stripping (d,p) reactions. One 1 = 2 and four I = 1 captures are considered. Optical potentials with rounded edges are used to distort the wave functions. In some cases the correlation is considerably changed from the pattern predicted by the plane wave Born approximation, and the distontion effects are strongly dependent on the direction of the emitted proton, and on the type of distortion assumed. Included is a general discussion of the theory of the (d,p gamma ) correlation. (auth)

Numerical Evaluation of Deuteron Stripping Cross Sections and Polarizations

The distorted-wave Born approximation is applied to deuteron stripping reactions. Optical potentials with rounded edges are used to distort the wave functions used in our calculations. It is found possible to get a fair fit to the ($d, p$) cross section in four cases and to the ($d, p$) polarization in one case with this treatment without introducing a cutoff.

Use of Antisymmetrized Wave Function for Deuteron Stripping Reaction

The general S matrix of nuclear reaction is derived by the method of second quantization in order to take account of antisymmetrization of the total system. As an example of the general theory, a deuteron stripping reaction is treated. The amplitude obtained by this method is compared with those obtained by other theories in this reaction. The amplitude of this reaction is discussed for a special target which seems to demonstrate the effect of antisymmetrix zation most clearly. In the case of O/sup 17(d,p)O/sup 18/ the effect of antisymmetrization becomes comparable with the direct part. (auth)

Spin of103Ru by Deuteron Stripping

The ground state of Ru/sup 103/ is predicted by the shell model to have a spin of 7/2 or 5/2 with even parity. Deuteron stripping reactions in Ru/sup 102/ were used in making direct measurements of spins for comparison. The measurements indicate that if the ground state of Ru/sup 103/ is formed by an 1/ sub n/ = 2 transition from an eveneven nucleus, it must have spin and parity of 3/ 2/sup +/ or 5/2/sup +/. If the transition 1/sub n/ = 3, the spin on parity are 5/ 2/sup -/ or 7/2/sup -/ Proton angular and energy distributions from the Ru/sup 102/(d p) reaction are included. (D.E.B.)

Tissue doses of fast and ultra-fast neutrons

An investigation has been carried out of depth doses in irradiation of tissue-like dummies (water, paraffin) with broad beams of fast and ultra-fast neutrons generated in the 1.5 meter cyclotron by bombarding a thick beryllium target with deuterons accelerated to 13 Mev (the reaction Be9 (d, n)B10) in the six-meter synchrocyclotron by bombarding a thick copper target with deuterons accelerated to 280 Mev (deuteron stripping reaction), and in the six-meter synchrocyclotron by bombarding a beryllium target with protons having an enervy of 480 Mev (proton charge-exchange reaction).

Shape effects in deuteron stripping on spheroidal nuclei

The geometrical effect of the spheroidal shape of strongly deformed nuclei on the angular distributions from deuteron stripping reactions is discussed. The usual boundary conditions are assumed, not on a Butler sphere of radius r 0, but rather on a corresponding spheroidal boundary. This gives rise to contributions to the reaction amplitude, additional to the “spherical” parts, which correspond to angular momenta L different in general from the orbital angular momentum l of the captured nucleon. They do not, however, violate the strong coupling model selection rule L ≧ |K f −K i |− 1 2 ; in particular L = 0 can only occur if |K f −K i | = 1 2 . These shape contributions are in general rather small, but must be considered when attempts are made to correlate experimental widths with the nuclear collective model and to detect small configuration mixing effects.

Deuteron stripping with polarized deuterons

In order to estimate the effect of using polarized deuterons on the left- right assymetry in the angular distribution of nucleons from deuteron stripping reactions, the distorted-wave Born approximation has been used. Spin-orbit coupling has been neglected. (W.D.M.)

Predictions of the distorted wave theory of deuteron stripping reactions

The distorted wave theory of stripping is presented in a rather general form, and the degree of generality is examined. The spin polarisation of (d, p) protons and the correlation function of de-excitation γ-rays are expressed on this theory as functions of statistical tensors ϱ kq which can in principle be calculated given the details of the process (wave functions, interaction potential etc.). The form of the polarisation and correlation are investigated, and it is shown what features of these are characteristic of the theory in general as distinct from its details. In this way experimental tests are devised to find whether observed results are compatible with stripping theory of this type. The tests consist in relations predicted between observed “experimental parameters”. The cases l = 1 and 2 ( l = orbital angular momentum of captured nucleon) are discussed fully.

Direct Nuclear Reactions

It is the contention of this paper that the large majority of nuclear reactions which proceed to a low-lying level of the final nucleus are predominantly direct reactions with stripping-like angular distributions. It is seen that reactions of the form ($n, p$), ($p, {p}^{\ensuremath{'}}$), ($\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}}$), ($\ensuremath{\alpha}, p$), etc. have essentially as much chance of proceeding directly as does the deuteron stripping or pickup reaction. This latter reaction no longer appears in a category of its own, but merely as one example of a whole gamut of types of reactions which proceed via a characteristic direct process. Differential cross sections for the general class of direct reaction are calculated, and closed-form expressions obtained by means of the same approximations originally employed for the deuteron stripping reaction. It is seen that the angular distributions are dependent on the spins and parities of the initial and final nuclei involved, and are thus capable of yielding information regarding these properties; moreover the absolute magnitudes are capable of yielding interesting information concerning nuclear structure. Comparisons between theory and experiment are made for a few typical reactions.

Deuteron Stripping and the Compound Nucleus

Deuteron stripping (d, p) reactions are investigated as corrections to the ordinary formal theories of nuclear resonance reactions, based on the compound nucleus model, in which the decaying tails of the internal wave functions of various reaction products are neglected. The amplitude for a (d, p) stripping reaction is shown to be due to the ov.erlapping of the decaying tail of the deuteron internal wave function and the wave function of the neutron trapped in the target nucleus. It differs from the Butler's stripping amplitude in that the contributions from the configurations in which the proton is within the range of the interaction between the proton and the target nucleus or between the proton and the neutron interacting with the target nucleus, are properly included in the amplitude for the (d,p) reaction due to the formation and the subsequent decay of the compound nucleus. The effects of the compound nucleus formation on the angular distribution of emerging protons are also discussed in connection with the interpretations of some phenomenological calculations hitherto presented. As the formulation is given in a general way, it can be applied also to other cases than the deuteron stripping reaction, such as (p, d) pick-up, (n, p) direct or (t, d) stripping reactions.

Approximation for Deuteron Stripping Reactions on Heavy Target Nuclei

Approximation for Deuteron Stripping Reactions on Heavy Target Nuclei

Deuteron Reactions and theA=14Polyad

Possible deuteron stripping and pickup reactions involving various states for $A=14$ and the two one-hole states for $A=15$ are discussed in detail. They would give considerable information about the $A=14$ wave functions (particularly the ${\mathrm{C}}^{14}$ and ${\mathrm{N}}^{14}$ ground states) and also some valuable measurements of the basic single-particle Butler cross section.

Deuteron Stripping Reactions and Nuclear Shell Structure

The purpose of this paper is to show that the mixing of the configurations can successfully be applied to deuteron stripping reactions when the angular distribution is characterized by two orbital angular momenta, and conversely that the percentage of the configurations can be determined from the observed relative heights of two peaks in the angular distribution. The calculations are based upon the perturbation theory. The agreement between the calculated and observed angular distributions is good. For the reaction F19(d, p)F20, the unexpectedly small reduced widths are reasonably explained from the standpoint of configuration mixing. Through the investigation of Mg25(d, p)Mg26*, we found that spin assignment of the first excitetd state of Mg26 is favourable to 2. Finally we discuss the relations between the type of mixing of the configuration used here and other types introduced to explain the quadrupole moments of odd nuclei.

Stripping and pick-up reactions — Experimental

Synopsis Recent advances in the techniques for measuring angular distributions of protons and neutrons from deuteron stripping reactions are described. These involve magnetic analysis in the case of protons and the use of scintillation counters for neutrons. Little work has so far been done on pick-up reactions. The use of angular distributions for the assignment of spins and parities to resultant nuclear states requires a certain amount of care and experience; the nuclear radius is to some extent an adjustable parameter to be used with caution. Relative values of the stripping cross section for different levels of the same nucleus often provide useful hints regarding the structure of the levels. Direct comparison of reduced widths of corresponding states of mirror nuclei have shown fair agreement. A considerable amount of experimental work is being done in an effort to throw some light on the mechanism of the stripping process. Measurements of excitation functions sometimes show resonances which are more prominent at the stripping peak than at large angles, indicating interference between stripping and some other process. Further useful information is being obtained from measurements of ( d , pγ) angular correlations and of the polarisation of the protons.

Stripping Reactions and Nuclear Shell Model

It has been pointed out by many authorsll2l that the angular distributions from certain (d, p) and (d, n) reactions should give a sensitive measure of the accuracy of the nuclear structure in ascribing definite orbital angular momentum states to nucleons in a nucleus. This possibility is due to the facts that these reactions proceed mainly by means of a stripping process and that their angular distributions are characterized by the orbital angular momentum l with which the captured particle can be accepted into the appropriate final state. The theoretical expression of the differential cross section for the deuteron stripping reactionll includes the summation over all values of l, allowed by the selection rules. Therefore, each allowed value of l produces a peak in the angular distribution without interfering one another, the peaks corresponding to different l being quite separated. The theoretical angular distribution shows a pronounced peak at small angles, and the maximum resulting from the smallest allowed l is of much larger magnitude than the others. The heights of the the peaks decrease rapidly and the peaks move progressively toward the large angles as l increases. The investigations on the validity of the shell model by the deuteron stripping reaction are necessarily restricted to the lower l values. If the experimental angular distribution is characterized by two l values, it shows evidently the deviation from the pure shell model, i.e., the admixture of orbital angular momentum states. Recently, the necessity3> of the mixing of the configurations in nuclei was pointed out in the studies on the first excited states in the even-even nuclei and on {3-decay with anomalous ft-values. The mixing of the configurations was applied with much success to explain the deviations of the magnetic moments4)5) from the Schmidt limit in odd-A nuclei, and quadrupole moments,6> and the {3-decay and r·transition of the forbidden types. The purposes of this note are to show that the mixing of the configurations can be applied to the deuteron stripping reactions also with success when the angular distributions are characterized by two l values, and that we can determine the percentage of the mixing of the configurations from the observed relative heights of the peaks reversely. We have derived the (d, p) differential cross section in the modified Born approximation. As the result, we have

Angular Momentum Coupling in Deuteron Reactions

Information about nuclear coupling schemes which can be derived from relative cross sections in deuteron stripping and pickup reactions in light nuclei is considered. In a few cases, experimental results are applied to give a determination of the intermediate-coupling parameter.

Theory of (d, p) and (d, n) Reactions II: Coulomb Corrections and Numerical Results

The results of an earlier publication are generalized to take account of the effect of the Coulomb field on the differential cross section in a deuteron stripping reaction. The results, which are expressed in analytical form, have been compared in detail with the observations in two reactions using 9Be as target nucleus at low energies.

The Theory of the Deuteron Stripping Reactions

The deuteron stripping reactions are analyzed from the point of view of the many-body problem. A rigorous formal solution is given. From this it is shown how assumptions less restricted than Butler's can be employed to reduce the many-body interactions to those of a deuteron moving in a potential well. At this point, the relation to previous theories is readily established. The present theory might be termed "the optical model" of the stripping reactions and represents a considerable generalization of current theories.

Angular Distribution of -Radiation Following a Deuteron Stripping Reaction

The angular distribution of γ-radiation from a deuteron stripping reaction is given as a Legendre series W(θ) = ΣνAνPν (cos θ). The coefficients are given in terms of the total angular momentum (orbital plus spin) of the captured nucleon and fully tabulated. Analysis of observed distributions can then test j-j shell model assumptions. Cascades are discussed and a general theorem for the angular distribution of the nth radiation of a cascade is stated in an Appendix. Formulae are given relating the parameters of this paper to those used in the channel spin formulation. Their values when the nuclei obey L-S coupling rules are also given. Some other applications of the theory are indicated and results of interest to experimentalists are summarized.