Momentum Transfer In Reactions Research Articles

Short-range expansion for the quantum many-body problem

In this work we derive a systematic short-range expansion of the many-body wave function. At leading order, the wave function is factorized to a zero-energy s-wave correlated pair and spectator particles, while terms that include energy derivatives and larger orbital angular momentum two-body functions appear at subleading orders. The validity of the expansion is tested for the two-body case, as well as the many-body case, where infinite neutron matter is considered. An accurate and consistent description of both coordinate-space two-body densities and the one-body momentum distribution is obtained. These results show the possibility to utilize such an expansion for describing different observables in strongly-interacting many-body systems, including nuclear, atomic and condensed-matter systems. This work also opens the path for a systematic description of large momentum transfer reactions in nuclear systems sensitive to short-range correlations, provides a link between such experiments and low-energy nuclear physics, and motivates measurement of new observables in these experiments.

The large momentum transfer reaction 12C( p,2 p + n) as a new method for measuring short range NN correlations in nuclei

The reaction 12C( p,2 p + n) was measured for momentum transfers of 4.8 and 6.2 (GeV/c) 2 at beam momenta of 5.9 and 7.5 GeV/c. We measured the quasi-elastic reaction ( p,2 p) at θ cm ⋍ 90°, in a kinematically complete measurement. The neutron momentum was measured in triple coincidence with the two emerging high momentum protons. We present the correlation between the momenta of the struck target proton and the neutron. The events are associated with the high momentum components of the nuclear wave function. We present sparse data which, combined with a quasi elastic description of the ( p,2 p) reaction and kinematical arguments, point to a novel way for isolating two-nucleon short range correlations.

Bound state and continuum production in large momentum transfer reactions

The cross sections for pp → pnπ + and pd → pdπ 0 are related to those for the corresponding reactions producing bound deuterons and 3He's respectively. The large momentum transfers in the reactions involve short range operators and under these conditions the predictions of continuum cross sections from bound state data are largely model independent at low energies and the constraints can be useful in extrapolations to threshold.

Measurement of high momentum transfer reactions by recoil detection at a cooler ring

Abstract A system for the measurement of medium-energy, high-momentum transfer reactions via detection of the heavier ion products has been developed. The system consists of a parallel grid avalanche counter, a proportional counter, and a large-area microstrip silicon detector array, all attached to a large-gap dipole magnet that bends the primary beam through 6° and sweeps the recoil ions into the detection system. The detector stack measures the energy, time-of-flight, nuclear charge, mass, and angle of recoil-ion emission products. Ray tracing gives the emission angle of the recoil ions at the target. The system was installed at the Indiana Cooler Ring and its advantages and use in a storage ring environment are discussed. Preliminary results of differential cross section measurements for the reaction 12C(p, π+)13C at Tp = 166 and 294 MeV are presented.

The Reggeon trajectory in exclusive and inclusive large momentum transfer reactions

A fundamental prediction of perturbative QCD is that the Reggeon trajectories α ϱ ( t) and α A 2 ( t) governing charge exchange reactions at high energies s ⪢ − t must monotonically approach zero at large spacelike momentum transfers. The asymptotic prediction lim − t→∞ α R ( t) = 0 reflects the fact that a weakly interacting quark-antiquark pair is exchanged in the t-channel. However, measurements of the inclusive processes π − p → π 0 X at s ≅ 300 GeV 2 and 8 GeV 2 > − t > 2 GeV 2 indicate that the effective ϱ trajectory becomes negative at large − t. We resolve the apparent contradiction between the perturbative QCD predictions and the experimental data by showing that the hard QCD part of the trajectory is weakly coupled and that its contribution will be hidden until much higher energy. We also show that Reggeon contributions to exclusive and inclusive mesonic exchange hadron reactions can be systematically studied in perturbative QCD. In particular, the Reggeon contributions to the reaction π − p → π 0 X and π − p → π 0 n is discussed in detail.

Target excitation and angular momentum transfer in reactions of E/A=11.9 MeV 28Si with 181Ta from 4 pi charged particle, neutron, and gamma -ray multiplicity measurements.

The conversion of kinetic energy into target-like fragment excitation and orbital angular momentum into fragment spin has been studied in the reaction 333 MeV $^{28}\mathrm{Si}$ with $^{181}\mathrm{Ta}$. The light charged particles were detected in a small, highly segmented, 4\ensuremath{\pi} phoswich detector system placed in the spin spectrometer, a 4\ensuremath{\pi} NaI array which served as a neutron and gamma detector. Multiplicities of light charged particles and neutrons detected in coincidence with projectile-like fragments indicate that the excitation energy of the target-like fragment increases as the kinetic energy of the projectile-like fragment decreases through the quasielastic region and tends toward saturation as the kinetic energy of the projectile-like fragment approaches the kinetic energy corresponding to complete damping. Measurement of the \ensuremath{\gamma}-ray multiplicity in coincidence with the projectile-like fragments indicates that the angular momentum transferred to the target-like fragment increases with decreasing mass of the projectile-like fragment for the quasielastic energy region in contrast to the energy region corresponding to completely damped processes where the angular momentum of the target-like fragment decreases with increasing mass loss from the projectile. The influence of preequilibrium processes on both excitation energy and angular momentum transfer to the target-like fragment is discussed. These data present further evidence that l waves below the entrance-channel critical angular momentum for fusion must contribute to the nonfusing reaction channels.

From chromodynamics to hadron physics towards nuclear physics

This session summary consists of 3 parts. Part I (M.Chemtob) proposes a discussion of the mesonic action approach to QCD and presents predictions for the skyrmion content in flavor, spin and linear momentum. Part II (B.Pire) discusses an application of the quark-diquark model of baryonic structure to moderate momentum transfer reactions. Part III (N.Isgur) discusses the limits of applicability of the perturbative QCD predictions for the pion and nucleon electromagnetic form factors.

Measurement of high momentum transfer reactions by recoil detection

A method is described for studying reactions at medium energies by measuring the magnetic rigidity, time of flight, and energy loss of the resulting recoil products. The method works best for reactions with two-body final states where one of the outgoing particles is relatively light. A magnetic spectrometer with a special focal plane detector has been used. The detector consists of two position sensitive parallel plate avalanche counters and two proportional counters. Differential cross sections for the 12C(p, π+13C reaction at recoil angles which correspond to the pion being emitted at a backward angle in the center of mass have been measured at bombarding energies of 166 and 186 MeV. Data were also obtained for previously unobserved 12C(p, π0)13N reaction. Several advantages of the method are discussed.

Symmetric splitting for the system 32S+238U at energies near and below the barrier.

The total capture cross section for the system /sup 32/S+/sup 238/U has been measured at energies from 0.93 to 1.08 times the s-wave interaction barrier by detecting coincident fission fragments following full momentum transfer reactions. The subbarrier cross section cannot be reproduced by a one-dimensional barrier penetration model. Using a quantum mechanical coupled channels model, good agreement is obtained. The measured angular distributions of fission fragments were compared to the predictions of saddle and scission point transition state theory. Saddle point transition state model calculations fail to reproduce the data, while scission point transition state calculations are in agreement with their qualitative trend. Evidence for nonequilibrium processes is presented.

Diquarks in exclusive reactions at large momentum transfer

Following many theoretical and experimental indications we assume that diquarks, in certain intermediate energy regions, can act as quasi-elementary constituents and take part in large momentum transfer reactions. We apply the idea to large angle exclusive interactions and show that diquarks could explain the whole amount of intriguing polarisation data in proton-proton elastic scattering and πp→ϱp reactions. The behaviour of the electromagnetic form factors of the nucleon is also discussed in the diquark model.

A model for low-pT hadronic reactions with generalizations to hadron-nucleus and nucleus-nucleus collisions

We present a model for hadronic low transverse momentum transfer reactions based upon a phenomenological treatment of a hadron as a vortex line in a colour superconducting medium. The predictions of the model are in agreement with the earlier successful model for the quantum number flows in the hadronic fragmentation regions while the present model also provides a number flows in the hadronic fragmentation regions while the present model also provides a consistent treatment of the central rapidity region. The model can also be applied to hadron-nucleus and nucleus-nucleus collisions.

THE CORRELATION OF LINEAR MOMENTUM AND ANGULAR MOMENTUM TRANSFER IN THE REACTIONS OF 310 MeV 16O WITH 154Sm

From co~nc~dence measurements between projecttle fragments or heavy residues and thetr assoc~ated Y-rays, we ave der' ed the angular momentum transfer In the incomplete fusion reactions of 310 MeV ''0 wtth 'Sm as a functton of !,near momentum transfer. The results have been compared with recent model predictions. Correlated measurements of linear momentum and angular momentum transfer in heavy ion collisions offer the possibility of delineating the part~al wave dependence of domlnant reaction mechantsms such as complete and incomplete fusion. Th~s allows one to test various theorettcal models which treat incomplete fusion such as the sum-rule model of Wilczynski(ll. the geometric overlap model of Harvey (2,3) and the more mtcroscoplc models, based on nucleon-nucleon ~nteractlons, proposed by Harvey (4) and by Cole (51. EXPERIMENTS: We have deduced the correlation bet een linear momentu transfer and angular momentum transfer in the reactions of 310 MeV '0 projectiles with m4Sm from two separate experiments performed at Texas AM (2) Measurements of the average y-ray multiplicity (using an 8-element Nal multiplicity filter) in coincidence with a microchannel plate - silicon detector time-of-flight system to measure the velocity of recoiling heavy residues. Linear momentum transfer was derived in the first experiment from the energies of the projectile-like fragments with corrections for missing momentum carried away by unobserved particles and in the second experiment from the residue velocities. Angular momentum transfer was derived from total gamma energy or gamma multiplicity, respectively. These two measurements taken together yield data that span the full range of fractional momentum transfer from 0 to 1. Details of the experiments will be given in a full article to be published elsewhere.

Angular Momentum Transfer in Reactions Induced by 14N Ions on 154Sm

The angular momentum input in reactions induced by 151 MeV 14N ions on 154Sm has been investigated by measuring the gamma-ray multiplicity in coincidence with emitted charged particles. The average multiplicity of gamma-ray cascades following the emission of protons, deuterons and tritons in reactions leading to 158Er amounts to 17.5 which is far below the value 31, earlier reported for a bombarding energy of 167 MeV. Predictions by Wilczynski's sum-rule model for complete and incomplete fusion reactions combined with statistical evaporation of particles are in good agreement with the present results.

Nuclear structure effects in high momentum transfer reactions

It is shown that, at large momentum transfers, one can extract nuclear structure information from the response (function) of the nucleus to an external scalar probe by factorizing the on-shell form factor associated to the struck nucleon. This result, derived both for elastic and inelastic scattering, arises from compensations between off-shell effects and exchange current effects generated by the (local) nucleon-nucleon interaction. The corrections to this on-shell factorization are in general found to be small at large momentum transfers. The role of the final state interaction in the nuclear transition form factor is then investigated and it is shown how one can, for instance, correct the orthogonality defect introduced by using a plane wave approximation for the struck nucleon.

Compound nucleus fission at high angular momentum studied in the reactionXe132+Si30

Reaction products from the bombardment of $^{132}\mathrm{Xe}$ onto $^{30}\mathrm{Si}$ at energies between 5.4 MeV/u and 8.2 MeV/u have been measured by a time-of-flight system combined with an ionization chamber. At all energies fission fragments are found to be well separated from deep inelastic reaction products. The rapidly increasing excitation function for fission shows an onset at $65\ensuremath{-}70\ensuremath{\hbar}$. This value and an ${l}_{\mathrm{crit}}$ of $98\ensuremath{\hbar}$ at 8.2 MeV/u are compatible with the concept of a fissioning compound nucleus. However, at the highest bombarding energies the $Z$ distributions indicate the emission of charged particles which is difficult to reconcile with the idea of a fully equilibrated compound nucleus. Incomplete momentum transfer reactions (incomplete fusion) followed by fission are considered as an explanation for the strong increase of the width of the $Z$ distribution with excitation energy. Consequences for the formation of compound nuclei at high angular momenta are discussed.NUCLEAR REACTIONS $^{132}\mathrm{Xe}$+$^{30}\mathrm{Si}$; $\frac{E}{A}=5.4\ensuremath{-}8.2$ MeV/u; measured $Z$ and $A$ distributions of fission fragments and ${\ensuremath{\sigma}}_{\mathrm{fission}}(E)$; compound nucleus fission and nonequilibrium effects. Enriched target.

A selection rule on angular momentum transfer in reactions of the type [formula omitted

An analysis of 50 experimental data on polarization and correlations of polarization in the reactions π N→ϱΔ, ωΔ and KN → K ∗Δ, ϱΣ ∗, ΦΣ ∗ strongly suggests a pure ΔJ=1 transition at the baryon vertex. A plot for testing graphically the linear constraints of the selection rule ΔJ=1 is proposed.

Large Momentum Transfer Reactions and Composite Model

Large Momentum Transfer Reactions and Composite Model

Linear momentum transfer in reactions between 140-MeVHe4ions and heavy nuclei

The fission of $^{238}\mathrm{U}$, $^{209}\mathrm{Bi}$, and $^{197}\mathrm{Au}$ induced by 140-MeV $^{4}\mathrm{He}$ ions has been studied in order to investigate the target-projectile reaction mechanism. The fission-fragment angular correlation technique was used to measure the linear momentum transfer in these reactions. It is found that an upper limit of (49.3\ensuremath{\ge}4.4)% of the fission in $^{238}\mathrm{U}$ results from the complete fusion of target and projectile. The incomplete fusion component of the $^{238}\mathrm{U}$ fission cross section includes a large fraction of high linear momentum transfer events, presumably produced in reactions where preequilibrium decay and/or deep knockout reactions are highly probable. The fission of $^{197}\mathrm{Au}$ and $^{209}\mathrm{Bi}$ is found to proceed almost completely via a complete fusion mechanism at this energy. The complete fusion cross section for $^{238}\mathrm{U}$ reactions with 140-MeV $^{4}\mathrm{He}$ ions is compared with that predicted from semiclassical collision models derived for heavy ion reactions.NUCLEAR REACTIONS, FISSION $^{238}\mathrm{U}(\ensuremath{\alpha},f)$, $^{209}\mathrm{Bi}(\ensuremath{\alpha},f)$, $^{197}\mathrm{Au}(\ensuremath{\alpha},f)$, $E=140$ MeV; measured ${\ensuremath{\sigma}}_{f}$, fragment-fragment angular correlation; deduced linear momentum transfer distribution, ${l}_{\mathrm{crit}}$.

Large momentum transfer reactions, without partons

Three recent experiments involving large 4-momentum transfer are compared to predictions of the hadronic bremsstrahlung model, witho t partons.

Gamma-Ray-Multiplicity Measurements for (α,p), (α,α′), (d,α), (p,α), (d,p), and (p,p′) Reactions

Using a method introduced previously measurements were made of the $\ensuremath{\gamma}$-ray multiplicity ${N}_{\ensuremath{\gamma}}$ (the average number of $\ensuremath{\gamma}$ rays emitted in the decay of residual nuclei left by nuclear reactions) as a function of excitation energy ${E}^{*}$ for ($p,\ensuremath{\alpha}$) and ($d,\ensuremath{\alpha}$) reactions on $^{51}\mathrm{V}$, $^{56}\mathrm{Fe}$, and $^{57}\mathrm{Fe}$ targets; ($\ensuremath{\alpha},p$) reactions on $^{51}\mathrm{V}$, $^{56}\mathrm{Fe}$, $^{57}\mathrm{Fe}$, $^{58}\mathrm{Ni}$, $^{64}\mathrm{Ni}$, $^{93}\mathrm{Nb}$, and Ag; ($\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}}$) reactions on $^{51}\mathrm{V}$, $^{55}\mathrm{Mn}$, $^{56}\mathrm{Fe}$, $^{57}\mathrm{Fe}$, $^{59}\mathrm{Co}$, and $^{64}\mathrm{Ni}$; ($d,p$) reactions on $^{51}\mathrm{V}$, $^{55}\mathrm{Mn}$, $^{56}\mathrm{Fe}$, Ag, and $^{119}\mathrm{Sn}$; and ($p,{p}^{\ensuremath{'}}$) reactions on $^{56}\mathrm{Fe}$, $^{112}\mathrm{Sn}$, and $^{122}\mathrm{Sn}$. Bombarding energies ranged from 12 to 19 MeV. ${N}_{\ensuremath{\gamma}}$ was observed to be generally between 1 and 5 for ${E}^{*}$ between 3 and 10 MeV for the ($p,{p}^{\ensuremath{'}}$), ($d,p$), ($d,\ensuremath{\alpha}$), ($p,\ensuremath{\alpha}$), and ($\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}}$) reactions investigated, and somewhat higher for the ($\ensuremath{\alpha},p$) reactions. ${N}_{\ensuremath{\gamma}}$ increases with ${E}^{*}$, and is larger for higher angular momentum transfer reactions although it is not as much larger as angular momentum transfer considerations alone would suggest. (This can be explained as a level-density effect for compound-nucleus reactions---the average angular momentum of the states excited by the reactions is severely limited by the level-density spin-cutoff parameter.) The dependence of ${N}_{\ensuremath{\gamma}}$ on the average excess angular momentum of the residual nuclei was investigated using calculated spin distributions for the residual nuclei. This dependence is similar to that for neutron capture ${N}_{\ensuremath{\gamma}}'\mathrm{s}\ensuremath{-}{N}_{\ensuremath{\gamma}}$ increases with excess angular momenta for excess angular momenta of more than 2 or 3 units.