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Influence of nucleon mean-free paths on intranuclear cascade results
PHYSICS LETTERS
Volume 68B, number 5
4 July 1911
INFLUENCEOFNUCLEONMEAN-FREEPATHSON INTRANUCLEARCASCADERESULTS" J. GINOCCHIO Theoretical
Division,
Los Alamos
Scientific
Laboratory,
Los Alamos,
NM*,
USA
and M. BLANN Department
of Chemistry
and Nuclear Structure
Research
Laboratory
**, University of Rochester,
Rochester,
NY, USA
Received 1 April 1977 Results of the intranuclear cascade calculation are compared for 62 MeV protons on 89Y and 54Fe targets. Standard calculations and results with mean free paths increased fourfold are compared. The latter set gives poorer results versus experimental data due to an overestimate of nuclear transparency.
Recent discussion of alternate formulations for preequilibrium decay models has centered on the value required for the mean-free paths of nucleons in nuclear matter [ 1,2]. One approach uses the result of free N-N scattering cross sections corrected for the Pauli exclusion principle, or the mean-free paths given by the imaginary optical potential [3]. The other approach uses mean-free paths approximately four times those given by the Pauli corrected N-N scattering cross sections [4]. It is natural to seek a resolution of the question of the correct value of the mean-free path in other independent models. Along these lines a recent work has appeared in which it is claimed that an intranuclear cascade calculation which used larger (X 4) mean-free paths would be in agreement with reactions at incident energies of 62 MeV. A reply to this paper suggests that poorer, rather than better, agreement with experimental yields would result if the longer mean-free paths were used, as a consequence of nuclear transparency in the entrance channel [2]. Neither of the works referred to actually presented comparisons of cascade model results with the “standard” and lengthened mean-free paths. We do this in the present communication in view of the fact
* Work performed under the auspices of the U.S. Energy Research and Development Administration. ** Supported by a grant from the National Science Foundation.
that the two papers referred to above reached different conclusions as to which result is more nearly consistent with the intranuclear cascade model, and therefore as to the correct value to use for the mean-free path (mfp) parameter. The cascade code used was “Vegas” [5], which was run in the “stepno” option, in which reflection and refraction are ignored at the density step boundaries. The latter option was selected because it is most nearly consistent with the Bertini-ORNL code [6] results referred to in [l] and [2] . One set of calculations for 62 MeV protons on targets of s4 Fe and 89Y was performed without modification of the VEGAS code and a second set with all N-N scattering cross sections reduced to one-fourth the free scattering value. The calculated proton spectra, excluding the evaporation spectra, are compared with the experimental spectra of Bertrand and Peelle [7] in fig. 1. Reaction cross sections are summarized in table 1. Reference to fig. 1 shows that the cascade calculation gives poorer agreement with the experimental spectra when the longer value of the mfp is used. The unrealistically low total reaction cross sections which result (table 1) assures that a calculation which includes evaporation (which we have not) will underestimate total emission yields by more than a factor of two. The agreement of the standard cascade calculation with the 89Y(p, p’) spectrum is, in our opinion, excellent. The small discrepancy is wholly within the error due to calculating too low a total reaction cross section 405
4 July 1977
PHYSICS LETTERS
Volume 688, number 5
Table 1 Experimental and calculated total reaction cross sections Target
Expt. (mb) [ 81
Normal mfp 4
9OY 54Fe
1059 f 26 (90Zr) 733
928 f 16 678 f 13
X
normal mfp
467 f 12 mb 302 f 9mb
errors in computing total particle emission yields and spallation cross sections.
I
20
L
a
40
I
1
60
20
40
I
I I
E,SMeV)
Fig. 1. Comparison of experimental (Bertrand and Peelle) and calculated (p, p’) spectra. The intranuclear cascade code VEGAS is used with normal and four times normal nucleon mean-free paths.
(table 1). For the case of 54Fe the calculated spectrum is in poor agreement with the experimental result for the high energy (nonevaporation) portion of the spectrum. We cannot state the reason for the discrepancy; however, it is clear from fig. 1 that the agreement becomes poorer rather than better as a result of arbitrarily increasing the mfp fourfold. We conclude that lengthening the mfp by a factor of ~four in the cascade model gives poorer agreement with measured spectra in the 62 MeV incident energy range and will lead to greater than a factor of two
406
References
60
[II E. Cadioli, E. Gadioli-Erba, G. Tagliaferri and J.J. Hogan, Phys. Lett. 65B (1976) 311.
PI M. Blann, Phys. Lett. 67B (1977) 145. [31 M. Blann, Phys. Rev. Lett. 27 (1971) 337,700E;
28 (1972) 757; Nucl. Phys. A213 (1973) 570; Ann. Rev. Nucl. Sci. 25 (1975) 123. [41 E. Gadioli, E. Gadioli-Erba and P.G. Sona, Nucl. Phys. A217 (1973) 589; C. Birattari et al., Nucl. Phys. 201A (1973) 579. [51 K. Chen, Z. Fraenkel, G. Friedlander, J.R. Grover, J.M. Miller and Y. Shimamoto, Phys. Rev. 166 (1968) 949. [61 H.W. Bertini, Phys. Rev. 131 (1963) 1801; Cl (1970) 423; H.W. Bertini, G.D. Harp and F.E. Bertrand, Phys. Rev. C8 (1974) 2472. [71 F.E. Bertrand and R.W. Peelle, Phys. Rev. C8 (1973) 1045; reports ORNL 4450 (1969) 4469 (1970) Oak Ridge National Laboratory (unpublished). [8] J.J.H. Menet, E.E. Gross, J.J. Malanify and A. Zucker, Phys. Rev. C4 (1971) 1114.
Volume 68B, number 5
4 July 1911
INFLUENCEOFNUCLEONMEAN-FREEPATHSON INTRANUCLEARCASCADERESULTS" J. GINOCCHIO Theoretical
Division,
Los Alamos
Scientific
Laboratory,
Los Alamos,
NM*,
USA
and M. BLANN Department
of Chemistry
and Nuclear Structure
Research
Laboratory
**, University of Rochester,
Rochester,
NY, USA
Received 1 April 1977 Results of the intranuclear cascade calculation are compared for 62 MeV protons on 89Y and 54Fe targets. Standard calculations and results with mean free paths increased fourfold are compared. The latter set gives poorer results versus experimental data due to an overestimate of nuclear transparency.
Recent discussion of alternate formulations for preequilibrium decay models has centered on the value required for the mean-free paths of nucleons in nuclear matter [ 1,2]. One approach uses the result of free N-N scattering cross sections corrected for the Pauli exclusion principle, or the mean-free paths given by the imaginary optical potential [3]. The other approach uses mean-free paths approximately four times those given by the Pauli corrected N-N scattering cross sections [4]. It is natural to seek a resolution of the question of the correct value of the mean-free path in other independent models. Along these lines a recent work has appeared in which it is claimed that an intranuclear cascade calculation which used larger (X 4) mean-free paths would be in agreement with reactions at incident energies of 62 MeV. A reply to this paper suggests that poorer, rather than better, agreement with experimental yields would result if the longer mean-free paths were used, as a consequence of nuclear transparency in the entrance channel [2]. Neither of the works referred to actually presented comparisons of cascade model results with the “standard” and lengthened mean-free paths. We do this in the present communication in view of the fact
* Work performed under the auspices of the U.S. Energy Research and Development Administration. ** Supported by a grant from the National Science Foundation.
that the two papers referred to above reached different conclusions as to which result is more nearly consistent with the intranuclear cascade model, and therefore as to the correct value to use for the mean-free path (mfp) parameter. The cascade code used was “Vegas” [5], which was run in the “stepno” option, in which reflection and refraction are ignored at the density step boundaries. The latter option was selected because it is most nearly consistent with the Bertini-ORNL code [6] results referred to in [l] and [2] . One set of calculations for 62 MeV protons on targets of s4 Fe and 89Y was performed without modification of the VEGAS code and a second set with all N-N scattering cross sections reduced to one-fourth the free scattering value. The calculated proton spectra, excluding the evaporation spectra, are compared with the experimental spectra of Bertrand and Peelle [7] in fig. 1. Reaction cross sections are summarized in table 1. Reference to fig. 1 shows that the cascade calculation gives poorer agreement with the experimental spectra when the longer value of the mfp is used. The unrealistically low total reaction cross sections which result (table 1) assures that a calculation which includes evaporation (which we have not) will underestimate total emission yields by more than a factor of two. The agreement of the standard cascade calculation with the 89Y(p, p’) spectrum is, in our opinion, excellent. The small discrepancy is wholly within the error due to calculating too low a total reaction cross section 405
4 July 1977
PHYSICS LETTERS
Volume 688, number 5
Table 1 Experimental and calculated total reaction cross sections Target
Expt. (mb) [ 81
Normal mfp 4
9OY 54Fe
1059 f 26 (90Zr) 733
928 f 16 678 f 13
X
normal mfp
467 f 12 mb 302 f 9mb
errors in computing total particle emission yields and spallation cross sections.
I
20
L
a
40
I
1
60
20
40
I
I I
E,SMeV)
Fig. 1. Comparison of experimental (Bertrand and Peelle) and calculated (p, p’) spectra. The intranuclear cascade code VEGAS is used with normal and four times normal nucleon mean-free paths.
(table 1). For the case of 54Fe the calculated spectrum is in poor agreement with the experimental result for the high energy (nonevaporation) portion of the spectrum. We cannot state the reason for the discrepancy; however, it is clear from fig. 1 that the agreement becomes poorer rather than better as a result of arbitrarily increasing the mfp fourfold. We conclude that lengthening the mfp by a factor of ~four in the cascade model gives poorer agreement with measured spectra in the 62 MeV incident energy range and will lead to greater than a factor of two
406
References
60
[II E. Cadioli, E. Gadioli-Erba, G. Tagliaferri and J.J. Hogan, Phys. Lett. 65B (1976) 311.
PI M. Blann, Phys. Lett. 67B (1977) 145. [31 M. Blann, Phys. Rev. Lett. 27 (1971) 337,700E;
28 (1972) 757; Nucl. Phys. A213 (1973) 570; Ann. Rev. Nucl. Sci. 25 (1975) 123. [41 E. Gadioli, E. Gadioli-Erba and P.G. Sona, Nucl. Phys. A217 (1973) 589; C. Birattari et al., Nucl. Phys. 201A (1973) 579. [51 K. Chen, Z. Fraenkel, G. Friedlander, J.R. Grover, J.M. Miller and Y. Shimamoto, Phys. Rev. 166 (1968) 949. [61 H.W. Bertini, Phys. Rev. 131 (1963) 1801; Cl (1970) 423; H.W. Bertini, G.D. Harp and F.E. Bertrand, Phys. Rev. C8 (1974) 2472. [71 F.E. Bertrand and R.W. Peelle, Phys. Rev. C8 (1973) 1045; reports ORNL 4450 (1969) 4469 (1970) Oak Ridge National Laboratory (unpublished). [8] J.J.H. Menet, E.E. Gross, J.J. Malanify and A. Zucker, Phys. Rev. C4 (1971) 1114.