States Of Compound Nucleus Research Articles

The width of the giant dipole resonance built on excited states of Cu compound nuclei

Continuumγ- ray spectra from the decay of59Cu formed at an excitation energy of 100 MeV and angular momenta up to 43ħ by means of the reaction 190 MeV32S +27Al have been measured and analyzed. The parameters of the Giant Dipole Resonance (GDR) have been extracted using the statistical model. The derived GDR width confirms the sizeable broadening of this resonance in59Cu already reported in our earlier investigation at 77 MeV excitation energy (Jcrit=38ħ). Estimates of the GDR width have been performed in the adiabatic approximation. Predicted values account qualitatively for the experimental data of59Cu as well as of the heavier isotope63Cu, in which the broadening was not seen up to 77MeV excitation (Jcrit=35ħ). The present analysis demonstrates the strong sensitivity of the GDR to spin effects in this mass region.

Analysis of excitation functions from light ion induced reactions in the EXCLUSIVE INDEX model

The previously introduced EXCLUSIVE INDEX model allows to predict the population of 6 residual nuclei including the primary compound nucleus through two stages of the preequilibrium phase. The present version is limited to maximum two-nucleon emission. The preequilibrium ejectiles may reduce the brought-in rotational energy by a model of maximum angular momentum decoupling. Subsequent evaporation of protons, neutrons andα-particles is treated in the frame of the Weisskopf-Ewing ands-wave approximation considering pairing effects only in compound nucleus state densities. The sensitivity of essential preequilibrium parameters on the shape of calculated excitation functions is tested. The model predictions well compare to excitation functions fromp, d,3He and4He induced reactions including the large set from the reaction93Nb(4He,xn yp) up to 170 MeV bombarding energy. The general importance of two-nucleon preequilibrium emission is accentuated in several examples. The deduced preequilibrium parameters corroborate the results from the INDEX model analysis of nucleon spectra.

Analysis of excitation functions from light ion induced reactions in the EXCLUSIVE INDEX model

The previously introduced EXCLUSIVE INDEX model allows to predict the population of 6 residual nuclei including the primary compound nucleus through two stages of the preequilibrium phase. The present version is limited to maximum two-nucleon emission. The preequilibrium ejectiles may reduce the brought-in rotational energy by a model of maximum angular momentum decoupling. Subsequent evaporation of protons, neutrons andα-particles is treated in the frame of the Weisskopf-Ewing ands-wave approximation considering pairing effects only in compound nucleus state densities. The sensitivity of essential preequilibrium parameters on the shape of calculated excitation functions is tested. The model predictions well compare to excitation functions fromp, d,3He and4He induced reactions including the large set from the reaction93Nb(4He,xn yp) up to 170 MeV bombarding energy. The general importance of two-nucleon preequilibrium emission is accentuated in several examples. The deduced preequilibrium parameters corroborate the results from the INDEX model analysis of nucleon spectra.

Compound nucleus temperatures from particle and gamma ray emissions: Effects due to the temperature dependence of the level density parameter.

Partial widths and branching ratios, for neutron and gamma ray emission from compound nucleus states, are calculated using a temperature dependent level density parameter. The results show that the corresponding emission temperatures, extracted from calculated neutron and gamma ray spectra, differ significantly from values obtained with a constant level density parameter.

Polarization effects due to coupling of elastic to compound states

From a compound nucleus level-density-dependent imaginary potential an energy-and angular-momentum-dependent polarization potential is obtained by using the dispersion relation. The effect of coupling in this way the compound nucleus states to the elastic channel is to introduce a strongly attractive real polarization potential at small separation of the centers of mass of the colliding nuclei. The effective potential at distances around the strong absorption radii of the systems 16O+ 24Mg, 28Si, 40Ca at different energies above the barrier is very slightly modified. Thus, the elastic and fusion cross sections of these reactions are hardly affected by the polarization potential.

Doorway states and cross-section fluctuations in the 12C

It is suggested that the deviations from pure Hauser-Feshbach predictions found in the already published analysis of /sup 12/C(/sup 16/O,..cap alpha..) data might be due to neglect of important multistep compound contributions. An appropriate multiclass fluctuation analysis clearly indicates the presence of two correlation widths, which can be associated with the population of two classes of overlapping states: one made up of doorway states, revealed by the largest of the observed coherence widths, and another made up of compound nucleus states connected with the fine structure of the fluctuating excitation functions. This interpretation was reinforced by new measurements on both excitation functions and complete ..cap alpha.. spectra. In addition, comparison of these data with calculations based on the quantum statistical multistep compound theory confirmed the importance of precompound effects and shed light on the nature of such doorway states which were found to be made up of 5p-1h configurations. These results support the hypothesis of Voit et al. that the first interaction between such light heavy-ion systems is dominated by the formation of ..cap alpha..-particle doorway states.

C10and11B+12C reactions from 4 to 9 MeV/nucleon

Reaction products arising from the interaction of $^{11}$B${+\mathrm{}}^{12}$C and $^{10}$B${+\mathrm{}}^{13}$C have been studied in the energy range 4${E}_{\mathrm{lab}(\mathrm{B})9}$ MeV/nucleon. From the total fusion cross sections for the two entrance channels, the critical angular momenta have been extracted and then compared as a function of compound nucleus excitation energy. Even though a limitation in the fusion cross section was observed, no common limitation was found in the critical angular momenta for these two systems up to at least a $^{23}\mathrm{Na}$ excitation energy of 60 MeV. Above this excitation energy, the experimental uncertainties make this point less clear. Up to an excitation energy of 60 MeV in $^{23}\mathrm{Na}$, a fusion limitation based on reaching a critical density of compound nucleus states like the yrast or ``statistical'' yrast line cannot be responsible for the fusion cross section limitations observed for these entrance channels. The present data suggest that competing entrance channel processes are responsible for the observed fusion cross section limitations.

Chemically induced shifts of 235U and 234U neutron resonances

Transmission spectra were measured with the time-of-flight technique at the Dubna pulsed reactor for samples of metallic U, UO 2, U 3O 8, and UO 3 enriched in 235U, and were compared in the regions of nine low-energy resonances to observe chemically induced shifts. After elimination of contributions caused by different Doppler broadenings, the shifts are interpreted as changes of the mean-square charge radius for nuclei capturing neutrons. The 〈 r 2〉 of the compound-nucleus states show on average a weak diminution as compared with the ground-state value.

A new method for the determination of the compound nucleus coherence width at high excitation energy

The coherence width of the compound nucleus can be obtained from cross correlations of the energy spectra taken at different energies instead of the correlation function of the excitation function. In this way it is sufficient to cover an incident energy interval of the order of the compound nucleus width. We have applied this method to the reaction 12C + 28Si. The coherence width of 40Ca is found in reasonable agreement with previous determinations. Indication is obtained for the presence of a second (smaller) coherence width which could correspond to anomalous long-living compound nucleus states.

Spin dependence of the parity non-conserving neutron-nucleus interaction

We show that the spin dependence of the parity violating amplitudes can provide a clue to the precise origin of the large parity non-conserving effects observed in neutron scattering on nuclei. The polarization asymmetries for longitudinal and transverse polarization of the incoming neutrons allow the separation of these spin amplitudes. In the mechanism of parity admixing of the virtually excited compound nucleus states, the spin dependence of the weak amplitudes is determined by the spin dependence of the strong interaction amplitudes for the elastic channel of the decay of the p-wave resonance

Parity violation in neutron elastic scattering around compound nucleus resonances

The parity non-conserving asymmetry for elastic scattering of polarized neutrons in the energy region around compound nucleus resonances is considered. The mechanism of virtual excitation of the parity admixed compound nucleus state is used. The parity conserving elastic amplitudes are dominated by s wave, but the simultaneous presence of the p wave resonant state is crucial for the parity violating amplitudes. Effects for n- 117Sn scattering are at the level of 10 −5 –10 −6, with a very peculiar energy dependence around the s wave resonance.

A study of the formation of compound nucleus states by absorption of 30 to 90 MeV photons in Sn, Ce, Ta and Pb nuclei

From measurements σ ( j) ( E γ ) = Σ i = j i max σ( γ, in…) on four heavy nuclei (Sn, Ce, Ta, Pb) from 30 to 90 MeV with monochromatic photons one obtains the cross section for the formation of a compound nucleus state excited with the full energy of the absorbed photon. This cross section is compared with high energy extrapolation of the Lorentz line which fits σ(tot: E γ ) on the giant dipole resonance and with the absorption on a quasideuteron pair. A value 3.5 fm <λ < 8.5 fm is deduced for the mean free path of a fast nucleon in these heavy nuclei.

The scattering of slow neutrons by cobalt

Different techniques have been used to determine with slow neutrons the coherent scattering amplitude bc and the total scattering cross-section σsc of Co. We found values for the bound atom bc=2.78+0.04 fm and for the free nucleus σsc=5.95+0.05 barns.From these quantities, the spin state scattering amplitudes b+ and b− corresponding to the compound nucleus states of spin I+1/2 or I−1/2 have been determined as b+=−2.78±0.04 fm and b−=+9.91±0.06 fm. These results are not in agreement with previous data, but they are found to be consistent with data obtained from resonance parameters.

Complex nonlocal optical potential for neutron scattering fromPb208

A nonlocal energy-dependent imaginary optical potential is calculated for neutron scattering from $^{208}\mathrm{Pb}$ in the intermediate structure model with weak particle-vibration coupling. The energy range studied is 0-12 MeV and the partial waves considered are $l=0\ensuremath{-}4$. The corresponding contribution to the real potential has also been obtained and is relatively small; this potential is presented for $s$ waves. The imaginary potential is used to calculate the absorption cross section in this energy range for each partial wave. Both compound-nucleus and inelastic contributions to the potential and the absorption cross section are included. Below 5 MeV compound-nucleus contributions are dominant. Above this energy inelastic excitations based on single-particle resonances and compound-nucleus states based on giant resonances contribute, with the former being more significant. A comparison of the calculated absorption to experiment for $s$, $p$, $d$, and $f$ waves is made below the inelastic threshold of 2.6 MeV. The agreement, except for $p$ waves, is quite good in terms of the number of resonances and other significant details of the cross section. The calculated absorption cross sections up to 12 MeV are compared to the results from a phenomenological local surface-peaked imaginary potential. The nonlocal potential is also surface peaked and the details of its radial behavior for an arbitrary energy are given in a contour plot.[NUCLEAR REACTIONS $^{208}\mathrm{Pb}(n,n)$, $E=0\ensuremath{-}12$ MeV; calculated nonlocal imaginary optical potential and absorption. Comparison with experiment and with a local imaginary potential. Particle-vibration doorways.]

The five-nucleon system above the three-particle threshold

Compound nucleus states in 5 Li and 5 He have been investigated with the 3 He(d,p)pt and 3 H(d,n)pt three-particle reactions. The observed J π= 3 2 − states ( E X ≈20 MeV) can be understood, in analogy to the ground states of the A=5 system, by coupling a p 3 2 nucleon to the first 0 + excited state of 4 He .

Test of the independence hypothesis and isospin conservation in compound-statistical reactions

Abstract Energy spectra and angular distributions of protons and α-particles emitted in the decay of 56 Fe, 60 Ni, 63 Cu, 64 Zn, and 66 Zn were measured. These compound nuclei were produced with a given excitation energy by irradiation of appropriate targets with 14.0 MeV protons and 15–19 MeV α-particles. The proton spectra featured a low-energy peak ascribable to the (p, np) or (α, np) reaction as well as a higher energy peak due to the (p, p') or (α, p) reaction. These peaks were sufficiently well resolved that differential cross sections could be obtained for the p, np, as well as α exit channels. The α and np exit channels were found to be free of precompound effects and are not affected by isospin conservation. Comparison of these particular cross sections for both entrance channels permits a test of the independence hypothesis provided a correction is made for the different angular momentum distributions in the entrance channels. When this correction is applied on the basis of the spin-dependent statistical theory it is found that the independence hypothesis is confirmed in all cases. Comparison of the p and α exit channels leads to values of the isospin mixing fraction, μ, between the T > and T states of the compound nucleus. The values of μ are 0.4±0.2 for all five compound nuclei and correspond to Coulomb mixing widths whose value is approximately 20 keV.

Studies in isobaric analog resonances: II. Fine structure

The properties of the fine structure observed in connection with isobaric analog resonances in the elastic scattering of protons are examined in terms of the damping mechanism for the analog state. The observed asymmetries of the strength function are shown to be associated with phase correlations between damping and escape amplitudes. Correlations of the necessary type will possibly result from the virtual coupling through the open channel between the analog states and the nearby compound-nucleus states of normal symmetry. A brief discussion of the possible role of doorway states in feeding the latter is also given.

A model for the study of the interference of the direct and compound-nucleus reaction mechanisms

A model is proposed for the investigation of the interference of direct and compound-nucleus reaction mechanisms in the inelastic scattering of nucleons. The continuum eigenfunction is considered to consist of a sum of two types of components: Product functions represent the nonlocalized open-channel or scattering components. Closed-channel or compound-nucleus components are represented by localized functions. The direct reaction mechanism is characterized by the set of matrix elements of the nucleon-nucleus interaction that couple two open-channel components. The compound-nucleus reaction mechanism is characterized by the matrix elements that couple open- and closed-channel components. The formal development of the above model is essentially a simple application of Feshbach's unified theory of nuclear reactions. However an additional “surface-transition model” is employed, in which the coupling of the various open- and closed-channel components is restricted to occur at one value of the nucleon-nucleus separation. Within this model, the effective Schrödinger equation is completely solvable and an analytic expression for the collision matrix is derived. This expression indicates clearly the dynamical interference between the reaction mechanisms; namely, it indicates the nonlinear manner in which the two mechanisms contribute to the collision matrix. The collision matrix is further investigated in two situations. The case of an isolated compound-nucleus state is considered and the departures from the form of a direct term plus Breit-Wigner term are examined. The case of a dense set of overlapping compound-nucleus states is also treated. Here the energy-averaged collision function is compared to that which would arise in the absence of any compound mechanism. Insight is gained into the relation between such energy averages and the use of complex potentials in reaction theory. Implications of the dynamical interference for studies of statistical fluctuations is noted.

The two-step (p,2p) reaction

A formal theory of two-step (p,2p) reactions has been developed, based on a combination of the dispersion theory of compound-nucleus states and the formal reaction theory appropriate to a direct (p,p') reaction with final-state distortion. The formal theory yields an expression for the angular correlation between the two protons emerging from a two-step process involving an isolated intermediate state. This expression is obtained explicitly for the simplest plane wave Born approximation description of the (p,p') process. The effects of antisymmetric wave functions, neglected in the early parts of the paper, are discussed at the end in terms of the formal theory.

On the existence of an internucleon potential not conserving spacial parity

The asymmetry effects (as forward – backward (FB), left – right (LR) and parity non conservation (PNC)) observed in the fission induced by thermal and resonant neutrons on 233, 235U nuclei in the frame of the formalism of mixing states of compound nucleus with the same spin and opposite parities were explained. In this work new P resonance parameters from FB and LR effects in order to explain the observed asymmetries and PNC effect have been derived.The present study demonstrates by using the multilevel Breit – Wigner formalism that the resonance states observed in FB and LR measurements are just a result of multilevel interference between S resonances. Only new P resonances, not indicated in nuclear data atlases for neutron resonance parameters, are enough to describe the asymmetry effects.