Nucleon scattering to the continuum in terms of the two-fermion theory of multistep direct reactions

NUCLEAR PHYSICS A ELSEVIER

Nuclear Physics A 633 (1998) 446-458

Nucleon scattering to the continuum in terms of the two-fermion theory of multistep direct reactions A. Marcinkowski a,1, B. Mariafiski a, Z. Moroz a, J. Wojtkowska a, R Demetriou b a Soltan Institute for Nuclear Studies, Warszawa-Swierk, Poland b INFN, sezione di Pavia, Pavia, Italy

Received 13 November 1997; revised 14 January 1998; accepted 26 January 1998

Abstract Cross sections of the (p,xp) reaction on 93Nb were measured at an incident energy of 26.5 MeV and analysed together with the existing data for nucleon scattering between 18 and 26 MeV. The (p,p') and (n,n') emission spectra and angular distributions have been described consistently in the framework of the two-fermion multistep direct theory of Feshbach, Kerman and Koonin. We have confirmed the predictions following our earlier analyses that the strength of the effective nucleonnucleon interaction does not depend on the reaction channel provided that all pre-equilibrium reactions are included. The latter requires allowing for the giant resonances in continuum from the energy-weighted sum rules. The method applied avoids double-counting of collective and onestep direct excitations. (~) 1998 Elsevier Science B.V. Keywords: Nuclear reactions 93Nb(p,xp), E = 26.5 MeV; Measured o-(E ~, 0); 93Nb(p,xp), (n,xn),

E = 18-26 MeV; Analyzed o-(U) and o-(E~, 0) vs data; Statistical multistep theory PACS: 25.40.Ep; 25.40.Fq; 24.60.Dr; 24.60.Gv; 24.30.Cz

1. Introduction C o n t i n u o u s spectra from ( n , x n ) and ( p , x p ) reactions in the incident energy range 1 4 - 8 0 M e V are k n o w n to be a good tool for studying various p r e - e q u i l i b r i u m processes [ 1,2]. A c c o r d i n g to the most extensively used theory of Feshbach, K e r m a n and 1Correspondence to: Professor A. Marcinkowski, Department of Nuclear Reactions, Soltan Institute for Nuclear Studies, 00-681 Warszawa, ul. HoLt 69, Poland. 0375-9474/98/$19.00 (~) 1998 Elsevier Science B.V. All rights reserved. PII $ 0 3 7 5 - 9 4 7 4 ( 9 8 ) 0 0 1 2 8 - 6

A. Marcinkowski et al./Nuclear Physics A 633 (1998) 446-458

447

Koonin (FKK) [3], one can distinguish two kinds of such reactions, namely the multistep compound (MSC) reactions involving only quasibound states and the multistep direct (MSD) reactions that create states containing at least one particle in the continuum. It is assumed that the reactions proceed via a series of collisions initiated by the projectile and each of the collisions adds another particle-hole pair. After one or a few collisions, a direct reaction occurs when a particle survived in the continuum throughout the cascade, otherwise a multistep compound reaction takes place. In the low-energy part of the nucleon emission spectra the dominant contribution comes from the decay of the fully equilibrated compound nucleus (CN). On the other hand, elastic scattering and direct, iLnelastic excitation of collective states shape the high-energy part of the nucleon scatteriag spectra. The relative importance of the different processes varies strongly with the incident energy. In general due to the limited energy resolution the measured nucleon spectra appear to be rather structureless which renders an unambiguous decomposition into parts belonging to different reaction mechanisms a difficult task. This encounters many unresolved problems, e.g. the influence of strong multistep direct processes on the compound reactions [4-7] and the role of the direct collective reactions (DCR) [8-10] which have only recently been studied. These analyses have shown that it is important to study simultaneously the charge-exchange reactions that are free of the strong isoscalar collective excitations and the scattering reactions in order to arrive at a consistent theoretical description. In an attempt to perform such global analysis it was found that the (p,n), (n,p) and (n,n') reactions can be described in a fully consistent way in the framework of the one-fermion multistep reaction theory of FKK. The (p,p') data, however, could only be fitted by approximately doubling the strength of the effective interaction that normalizes the MSD cross sections. Several possible reasons for this were investigated in Ref. [ 11] but the difficulty still remained. It is the aim of the present paper to remove this difficulty by improving the MSD calculations for a set of complementary neutron and proton scattering data for the same target at the same energy. Such experimental data can hardly be found, as there are few (p,xp) measurements at 14 MeV, the energy at which most of the neutron cross sections were measured. Therefore we analysed the proton scattering data of Watanabe et al. [ 12] obtained at 18 MeV and the results of our measurements at 26.5 MeV together with corresponding neutron data, for the same niobium target often used as a standard.

2. The experiment The cross sections of the 93Nb(p,xp) reaction were measured at the compact C-30 cyclotron of the Soltan Institute for Nuclear Studies in Swierk. Protons of 26.5+0.2MeV energy were focused into a 70 cm scattering chamber and monitored by a Si(Li) detector of 5 mm thickness, placed at 90 ° with respect to the beam. The thickness of the niobium target was about 2 /xm. The proton emission spectra were measured with a movable

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A. Marcin~)wski et al./Nuclear Physics A 633 (1998) 446-458

Table 1 Differential (mb/srMeV) and integral (mb/MeV) cross sections for the 93Nb(p,xp) reaction at incident energy of 26.5 MeV Energy-out [MeV]

150 °

Angle-integr

60 °

90 °

120 °

2.5

0.25 4- 0.00

0.62 4- 0.01

0.52 4- 0.01

0.74 4- 0.01

5,9 i 1.8

3.5

4.104- 1 . 2 5

3.794-0.07

3.31 4-0.03

5.224-0.04

59,1 4- 15.1 79.54- 16.0

4.5

4.944- 1 . 4 7

5.374-0.10

4.944-0.05

8,074-0.07

5.5

4.764- 1 . 4 3

5.944-0.10

4.75 4-0.05

7.524-0.07

80.34- 15.0

6.5

4.344- 1 . 3 0

5.564-0.10

4.124-0.04

5.644-0.06

68.04- 10.5

7.5

3.864- 1 . 1 0

4.464-0.10

3.104-0.04

3.964-0.05

52.84-6.0

8.5

3.374-1.00

3.514-0.09

2.194-0.04

2.754-0.04

41.94-4.2

9.5

2.94 4- 0.88

2.38 4- 0.07

1.46 4- 0.03

1.93 4- 0.03

32.8 4- 3.3

10.5

2.974-0.10

2.054-0.07

1.054-0.03

1.424-0.03

29.34-2.9 26.0 4- 2.6

11.5

2.83 4- 0.10

1.68 4- 0.06

0.82 4- 0.02

1.03 4- 0.03

12.5

2.51 4- 0.10

1.40 4- 0.05

0.69 4- 0.02

0.80 4- 0.02

23.4 4- 2.3

13.5

2.23 4- 0.09

1.21 4- 0.05

0.57 4- 0.02

0.62 4- 0.02

20.9 4- 2.1

14.5

2,194-0.09

1.084-0.05

0.504-0.02

0,534-0.02

19.04- 1.9

15.5

2.184-0.09

0.974-0.04

0.444-0.02

0.444-0.02

18.04- 1.8

16.5

2.02 4- 0.09

0.88 4- 0.04

0.39 4- 0.02

0.36 -I- 0.02

18.2 4- 1.8

17.5

1.78 4- 0.08

0.77 4- 0.04

0.36 4- 0.02

0.33 4- 0.01

17.6 4- 1.8

18.5

1.79 4- 0.08

0.72 4- 0.04

0.33 4- 0.01

0.30 4- 0.01

16.3 4- 1.6

19.5

1.78 4- 0.09

0.69 4- 0.04

0.27 4- 0.01

0.27 4- 0.01

16.5 4- 1.7

20.5

1.48 4- 0.07

0.68 4- 0.04

0.21 4- 0.01

0.21 4- 0.01

14.2 4- 1.4

21.5

1.384-0.07

0.744-0.03

0.184-0.01

0.194-0.01

15.74-2.2

22.5

1.344-0.06

0.874-0.04

0.194-0.01

0.214-0.01

16.84-2.7

d E + E telescope consisting of two Si(Li) detectors at angles between 30 ° and 150 ° every 30 °. A 50 /xm thick d E detector and a 4 m m E detector were applied. During

the measurements an additional monitor was installed downstream from the scattering chamber that contained a beam foil scatterer and a 4 m m thick Si(Li) detector at 90 ° with respect to the beam. Scalers counting pulses from the monitors as well as summing all pulses from the telescope were used to estimate counting losses due to dead-time. Data from elastic and inelastic scattering of 12C were used to calibrate proton energies, together with alpha particles from 24tAm and ThC'. We found the spectra measured at 30 ° and 60 ° to contain background admixtures due to protons depositing some energy in the collimator edges [13]. The spectrum at 30 ° was disregarded and the one taken at 60 ° was corrected for this background. The results of our measurements are gathered in Table 1 together with the angle-integrated data obtained from Legendre polynomial fits. The errors attached to the double-differential cross sections are statistical only. The errors of the angle-integrated cross sections also contain the uncertainty of the Legendre polynomial fits and an overall systematic error of 10% due to the absolute normalisation to the optical model elastic cross section [ 14].

A. Marcinkowski et al./Nuclear Physics A 633 (1998) 446-458

449

3. The model cross sections of the direct non-elastic reactions

The non-elastic cross section of the MSD reaction to the continuum is a sum of the contributions due to collisions of the projectile with nucleons of the target nucleus, each collision exciting a l p lh pair. According to FKK these contributions are expressed by a convolution of the mean-squared matrix elements (IVM,M_1I2) of the residual interaction for the one-step transitions between subsequent states ( M - 1) and M. The cross section for a one-step reaction is [3],

a'2o"

morn1 k0 - - p~(U)(lvl,o(kl,ko)12) , t/U dg2 (2~'h2) 2 kl

(1)

with Pl (U) being the density of states of the residual nucleus after the first stage of the reaction. Usually one assumes that the final states are those of the l p l h pair just created, independent of the reaction stage spectators. The transition probability pl (U)(lvl,0(kl, k0)[ 2) can be decomposed into the probability for the incoherent excitation c,f l p l h states of density p~,~(U) [15] and that for the coherent excitation of collective vibrations or rotations of the nucleus [ 16], pl (U)([vl,0(kl, k0)12) ---- P I , I (U)(IClplh,o(kl, k0) DWBA[2)

+ ~

,l

~(U - h~oa)(Ira,0 (k~, k0)DWBAI2) •

(2)

The first term of the r.h.s, of Eq. (2) was accounted for when the applicable MSD cross section formulae of the FKK theory were derived in Ref. [ 17]. The one-step cross section for incoherent excitation of the quasi-particle states can be divided according to the contributions of different transferred orbital angular momenta l, and expressed by the DWBA angular distributions &r/d12, reduced by assuming a unit strength for the effective nucleon-nucleon interaction and averaged over several lp 1h shell model states compatible with a given orbital angular momentum transfer 1 and the excitation energy U cons![dered, d2°" - Z ( 2 I +

dU ds2

1

1)g2U x R2(1)Vo2

/ (d°" ) DWBAmi/ cr -~

.

(3)

Here the substitution pl,1 (U) = g2U with g = A l l 3 being the single particle state density follows from the state density expression of Williams [ 15]. The spin distribution R2(/) of the l p l h states in Eq. (3) acts as a weighting factor for the reduced DWBA cross sections which were routinely calculated with microscopic two-quasi-particle form factors and with an average, real effective interaction of Yukawa form of 1 fm range and strength V0. It must be pointed out that ~-]t(21 + 1)R2(/) = 1. The Milan group used Eq. (3) successfully in analyses of charge-exchange reactions [ :17,18] that are free of the strong isoscalar collective excitations. However, simulation of the isoscalar collective enhancement of nucleon scattering spectra in the framework of this model by parameter adjustment led to unsatisfactory results [5,19].

450

A. Marcinkowskiet al./Nuclear PhysicsA 633 (1998) 446-458

Finally, the second term of the r.h.s, of Eq. (2) was allowed for and the direct collective reaction (DCR) cross sections for excitation of vibrations have been explicitly calculated, in framework of the macroscopic DWBA model, and found to be just sufficient to restore the consistent description of experimental inelastic neutron scattering spectra [8]. In these calculations a simple macroscopic approach was applied [9],

do. n ~ DWBAmacr d2° : ~-~fl](n) \ ~ . ] a x fa[hwa(n),F] dE d ~ n,a

(4)

with the radial form factors foo(r) = -R[OUoo/OR], derived by deforming the phenomenological complex optical potential U0o of radius R, and the phenomenological deformation parameters fla of the excited one-phonon states n of energy hwa and multipolarity A. The term fa is the energy distribution function which is assumed to be Gaussian with a width F appropriate to the limited experimental energy resolution for the individual collective levels or Lorentzian with width typical of the giant resonances in the continuum. The effective flcR-a parameters for the giant resonances can be obtained by depleting the energy-weighted sum rules (EWSR), by the strengths of all individual vibrational levels of a given multipolarity ,t that were allowed for in the sum of Eq. (4). Two-phonon excitations can also be considered in cases when experimentally identified by means of radial form factors of second order in the deformation of the nucleus [20]. In order to avoid double-counting of the collective and MSD contributions Eq. (3) has to be carefully parametrized through a comparison with the charge-exchange reaction data which are free of the strong isoscalar collective excitations and which can be easily cleared of most of the isovector resonances, e.g. of the narrow isobaric analogue resonance. Such parametrization leaves only the incoherent MSD transitions. Recently, RPA and coupled channel calculations of the cross sections including collective excitations were also performed [ 10,21,22]. So far no distinction between neutrons and protons has been made. This one-fermion model appeared quite successful in describing consistently, yet fortuitously, the (p,n), (n,p) and (n,n') reactions using Austin's V0 = 28 MeV value [23]. The difficulties encountered when extending this analysis to (p,pt) reactions [ 11 ] renewed interest in the two-component theory that distinguishes between the two kinds of nucleons and the corresponding single particle state densities g,, = N I l 3 for neutrons and g,r = Z/13 for protons as well as between the effective interaction of like V~.~. = V,,,,, and unlike nucleons V,, ~-. The microscopic two-fermion MSD theory for continuum reactions was discussed in Refs. [10,11]. Assuming that the average DWBA matrix elements for neutrons and protons are the same, the one-step cross section to the lp 1h final states reads,

A. Marcinkowski et al./Nuclear Physics A 633 (1998) 446-458

451

where both the indices a and fl take the values 7r or v and P~r, A,, h= and h,, are the nurabers of respective particles and holes. The sum over a and fl is symbolic and contains two terms corresponding to p= = h= = 1, p,, = h,, = 0 with a = / 3 = 7"r and p= = h= = 0, pv = hv = 1 with a = 7r, /3 = v for proton scattering. For scattering of neulrons the two terms correspond to P,r = h~ = 0, p,, = h~, = 1 with a = /3 = v and p~ = h~. = l, p~, = h,, = 0 with a = v, /3 = 7, respectively. For charge-exchange reactions the sum reduces to a single term: P,r = h~, = 1, Pv = h~. = 0 for (p,n) and p,, = hT~ = 1, p~r = hv = 0 for (n,p) reactions, both with a = 7, /3 = v. P is the paritydistrib~Ltion factor that assures parity conservation in the DWBA calculations (see [ l 0] ). The reason is that the state density ffl,1 ( U ) = gp+hg~v+hU accounts for all lp lh states, includiag those that can only be excited by spin-transfer reactions, whereas the DWBA calculations follow the parity and angular momentum selection rules excluding spin-flip transitions that lead to non-natural parity states. This is in accord with the choice of a nucleon-nucleon interaction that consists of only a real central term of Yukawa form. Comparison of Eqs. (5) and (3) shows that for incident energies where only the one-step direct cross sections are used, i.e. below approximately 30 MeV it is possible to pertorm a one-component calculation and to estimate correction factors for cross sections that reproduce the effect of a neutron/proton distinction [ 11 ].

4. Calculations and comparison with experiment The MSC model calculations do not depend on the strength of the effective nucleonnucleon interaction since the microscopic entrance channel strength function of FKK [ 3 ] was replaced by its optical model value (transmission coefficients) [4]. In order to calculate the pre-equilibrium MSC and the related CN cross sections the optical model strength function was reduced by the amount of the direct non-elastic cross section. The gradual absorption at successive reaction stages was assumed [ 6,7 ], and the overall reduction of the optical model potential absorption cross section by the factors 0.70 and 0.60 at incident proton energies 18 and 26 MeV as well as by the factors 0.72 and 0.55 at incident neutron energies 20 and 25.7 MeV, respectively, was obtained by integrating Eqs. (4) and (5) for outgoing neutrons and protons. Several global nucleon optical potentials were tested in statistical model calculations in Refs. [ 11,24]. We have chosen the potential of Wilmore and Hodgson [25] for neutrons and that of Perey [ 14] for protons which proved well in calculations of lowenergy nucleon inelastic scattering cross sections and allow one to compare our results with previous analyses [5,11,19]. The pre-equilibrium MSC cross sections of FKK [3,6] were truncated so that emissions from collisions after M = 3 were included in the CN cross sections calculated according to the Hauser-Feshbach theory. The neutron/proton distinction was included in the correction factors that determine the number of excited particles being protons or neutrons at each reaction stage [6,19]. The density of the bound-particle-hole levels was calculated with the spin cutoff parameter 0 -2 = 0.24nA 2/3, appropriate for the in-

452

A. Marcinkowski et al./Nuclear Physics A 633 (1998) 446-458

I

I

I

I

!

I

I

I

93Nb(n,xn)

En=20 MeV 1000

[

> .13

E Z

100

o

i.r,..) iJJ 09

09 09

o

nO 10

1 0

2

4

6

8

10

12

14

16

18

20

NEUTRON ENERGY [MeV] Fig. 1. Comparison of calculated emission spectrum for the 93Nb(n,xn) reaction at 20 MeV with experimental data of Marcinkowski et al. [4]. The label CNI denotes the evaporation of primary neutrons and CN2, CN3 denote successive emission of two and three neutrons, respectively. CPN denotes secondary neutrons preceded by evaporationof a proton. DCR labels the sum of cross sections for population of the collective low-energy levels as well as of the low-energy octupole (LEOR), the quadrupole and the dipole giant resonances in the continuum. The thick solid line is the sum of all contributions including MSD and MSC cross sections.

termediate numbers of excited particles and holes (h = 5) involved in MSC processes, and the single-particle state density g = All3. In the Hauser-Feshbach CN calculations the level densities and the pairing energy shifts zl were taken from Gilbert and Cameron [26]. The spin cutoff was 0-2 = O.146A2/3[a(U- A)] 1/2 with the level density parameters a taken from a global systematics [27]. In the MSC model only nucleon emission is allowed for, but in the Hauser-Feshbach calculations emission of alpha particles was also taken into account. The optical potential for alphas was from Ref. [28]. The radiative widths in the Hauser-Feshbach formulae were composed of single-particle and of giant resonance strength functions for El, E2 and M1 transitions. The MSC and the CN calculations were performed with the help of the extended version of the EMPIRE code [29].

A. Marcinkowski et al./Nuclear Physics A 633 (1998) 446-458

453

1000

~1oo

>

z

© b-W 09 O3 10 (/3

© no

2

4

6

8

10

12

14

16

18

20

22

24

26

NEUTRON ENERGY [MeV] Fig. 2. The same as in Fig. 1 but for the 93Nb(n,xn) reaction at 26 MeV [33].

The two-fermion microscopic MSD cross sections were calculated according to Eq. (5;) using the DWUCK-4 code [30], with two quasi-particle form factors. Distorted waves were obtained from the global optical potentials [ 14,25]. The MSD cross section for nucleon scattering in (5) depends via the form factor on the choice V,,,,, = V~.~ = 12.7 MeV and V,,.~ = 43.1 MeV [23] of the real Yukawa effective interaction of 1 fm range, acting on the bound-state wave functions of a real Woods-Saxon potential The average single-particle state densities for protons g~ = Z/13 and neutrons g,, = NIl3, and the spin cutoff parameter o-2 = 0.28nA 2/3 were used for the l p l h states (number of excited particles and holes n = 2) involved in the MSD process. We took for the parity distribution of the state density P = 1/2 which implies that we assume only natural parity states to be excited. In order to keep the MSD computations within reasonable limits we took into account a limited range of transferred orbital angular momenta 1 = 0. • • 9 for each of the lp I h configurations of the shell model of Seeger [ 31 ], observing angular momentum selection rules and energy conservation. Our DWBA calculations using DWUCK-4 were corrected for the omission in the reaction amplitude normalisation in this code [10]. We included the (2jh + 1) multi-

454

A. Marcinkowski et al./Nuclear Physics A 633 (1998) 446-458

I

I

l

I

1oof

I

I

I

93Nb(p,xp) Ep=18MeV

> (1) t-~

Z

10

O Io

uJ Go Go Go O no 1

0.1

2

4

6

8

10

12

14

16

18

P R O T O N E N E R G Y [MeV]

Fig. 3. Comparisonof calculated emission spectrum for the 93Nb(p,xp) reaction at 18 MeV with experimental data of Watanabe et al. [12J. The label CPI denotes the evaporation of primary protons and CNP denotes secondary protons preceded by evaporation of a neutron. DCR labels the sum of cross sections for population of the collective low-energylevels as well as of LEOR, the quadrupole and the dipole giant resonances in the continuum. The thick solid line is the sum of all contributionsincludingMSD and MSC cross sections. plicative factor missing in the cross section for each shell model l p l h excitation, where l p l h states were binned into l MeV energy bins and the DWBA cross sections for population of these states that correspond to a given orbital angular momentum transfer l were averaged within each energy bin (see Eqs. (3) and ( 5 ) ) . This resulted in strong fluctuations of the emitted nucleon spectra that follow the distribution of the shell model l p l h states. Therefore the calculated MSD emission spectra were afterwards smoothed by averaging over 5 MeV energy intervals typical of the giant resonances. The DCR cross sections were calculated according to Eq. (4). For 93Nb we considered

jh is the total angular momentum of the hole. The final shell model

the weak-coupling model, in which a multiplet of final states results by coupling of a valence, odd proton with angular momentum I = 9 / 2 - to a single /-phonon of collective motion. Instead of identifying all members of the multiplet we calculated the cross sections for excitation of the one-phonon states in the even-even 92Zr nucleus for

A. Marcinkowski et al./Nuclear Physics A 633 (1998) 446-458

100

[

L

~

~

~

~

~

~

~

0

2

4

6

8

10

12

14

455

9~Nb(~,xp) ~ 3p En = 26.5 MeV

> 11.)

z © lw

10

©

16

18

20

22

24

26

PROTON ENERGY [MeV] Fig. 4. T'ne same a,~ Fig. 3 but for the 93Nb(p,xp) at 26.5 MeV. Closed circles show the results of the present experiment and the open circles are from Yoshioka et al. [34]. CP2 denotes successive evaporation of two protons.

which the deformation parameters of the low-energy levels were compiled in [8]. The effective deformation parameters /3GR-a for the giant 1-, 2 + and for the low-energy fraction (LEOR) of 3 - resonance were obtained by depleting the EWSR's by the strengths of all known vibrational levels of chosen multipolarity A. The energies of the giant resonances were taken from Ref. [32]. The cross sections for excitation of the giant resonances were spread according to a Loreatzian function (see Eq. (4)) with a typical width F = 5 MeV. The cross section:~ for the low-energy phonon states were also broadened in order to account for the spreading of the spectroscopic strength adopted from the weak-coupling model (270 keV) and for the limited energy resolution in the experiments (about 0.5 to 1.5 MeV depending on the experiment considered [4,12,33,34] ). Double-counting of the MSD and DCR cross sections was prevented by using in our MSD calculations the same parameters which proved successful in fitting the smooth (p,xn) reaction spectra and angular distributions [8,35] not affected by coherent col-

456

A. Marcinkowski et al./Nuclear Physics A 633 (1998) 446-458 100

I

I

I

I

I

Ein=20 MeV O

©

o

o

10

>

10

I

I

o

0

O Q

I

O

I

c9

I

n

~

o

Q O

CNI+CN2+MSC

I

I

MeV

I

Eout=3-4 MeV

I

I

Eout=11-12 MeV

E Z

0 I--

o

w o) 0

n~

o 1

DCR( 2

~

0.1 I

I

I

I

I

I

I

I

20

40

60

80

100

120

140

160

THETA CM

[deg]

Fig. 5. The calculated angular distributions of neutrons emitted in the 93Nb(n,xn) reaction compared with experiments 14,331. The incident and outgoing neutron energies are shown. DCR(LEOR) labels the cross section due to excitation of LEOR mainly, D C R ( 3 - ) and DCR(2 +) label the contribution due to excitation

of the first 3- state at 2.30 MeV and the contribution due to the 2+ states at 0.93, 1.85, 2.49, 2.90 and 4.43 MeV in 93Nb, respectively. The thick solid line is the sum of all contributions shown. lective effects. In this way the M S D cross sections for inelastic scattering of nucleons have been reduced thus leaving room that is necessary for the DCR cross sections. The results of calculations for neutron scattering are compared with the angleintegrated cross sections measured by Marcinkowski et al. [4,33] at incident neutron energies 20 and 25.7 M e V in Figs. 1 and 2, and those for proton scattering are compared with measurements of Watanabe et al. [12] taken at 18 MeV in Fig. 3. In the course of the present experiment Yoshioka et al. [34] have also measured the ( p , x p ) reaction cross sections at 26 MeV. These data agree well with our measurement as shown in Fig. 4. In Figs. 5 and 6 some of the calculated angular distributions are also compared with experiments. The theoretical emission spectra and angular distributions fit the data satisfactorily as follows from the two-fermion M S D calculations using the effective interactions between the like and the unlike nucleons taken from Austin [23]. This result completes a consistent analysis of all nucleon reaction-channels initiated by Refs. [ 11,35,36] and confirms the prediction that the strength of the effective interac-

457

A. Marcinkowski et al./Nuclear Physics A 633 (1998) 446-458

o o ~

{1)

o

,--, ~

o

~

-

-

Ein=18 MeV q ~ " - e . . - . . ~ Eout=9-10 c~ n ~ MeV CPI+MSC

0.1 10

I

I

I

I

I

I

I

I

Ein=26.5 MeV ..Q

E Z

O

1

tO

CPI+CNP+MSC

w

0

0.1

I

I

I

I

I

0

0

I

I

I

Ein=26.5 MeV ut = 16-17 MeV © D C R ( L E O R ) ~ ~

0.1 I

20

MSC

v

I

I

I

I

I

40

60

80

100

120

140

160

[deg] Fig. 6. The same but for the 93Nb(p,xp) reaction. Closed circles show the results of the present experiment and the open circles are from Refs. I12,341. THETA

CM

tion as determined from the folding model [23] does not vary with reaction channel provided all mechanisms of pre-equilibrium reactions namely the MSC, MSD and DCR are considered [ 7 - 9 ] . This conclusion is different from the results of previous analyses [ 10,24,34] in which the effective interaction strengths were adjusted to fit separately the neutron scattering, the proton scattering and the charge-exchange reaction data. It seems worth to mention at the end that we did prove that the two-fermion MSD model describes also the charge-exchange 65Cu(p,n) reaction data as measured by Holler ,zt al. [37] at 26.7 MeV. For example the angle-integrated MSD cross sections d o ' / d E = 0.68, 4.33, 7.94 and 11.78 m b / M e V obtained for outgoing neutron energies 22.5, 18.5, 14.5 and 10.5 MeV, respectively, describe satisfactorily the measured smooth neutron emission spectrum using consistently Austin's effective interaction strength.

Acknowledgements We wish to thank M.B. Chadwick, A.J. Koning and EE. Hodgson for valuable discussions concerning the MSD reaction model. We also gratefully acknowledge receiving some unpublished experimental data from Y. Watanabe.

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