Saturday 24 August 2019

Physics of Nucleon-Nucleus Scattering - Epilogue

Epilogue


In this book, extensive microscopic analyses of elastic scattering of protons at select energies in the range 10 MeV to 800 MeV and from diverse nuclei (3He to 238U) have been made as have fully microscopic model calculations of such coordinate space optical potentials describing proton-12C elastic scattering at 18 energies in the range from 40 to 800 MeV. Both differential cross section and analyzing power data have been predicted at all energies considered.
           
The complex optical potentials were formed by folding effective NN interactions with the density matrices of the ground state of the target nuclei. For 12C a complete  shell model calculation provided those density matrices. The effective interactions were obtained by mapping half-off-shell NN g matrices (solutions of BBG equations) associated with Bonn potentials supplemented above pion threshold by short ranged Gaussian NN optical potentials so that all NN scattering phase shifts to over 1 GeV were reproduced. The results of the g-folding process are complex, nonlocal proton-nucleus potentials. Solution of the integro-differential Schrodinger equations formed with those optical potentials resulted in good to excellent fits to elastic scattering data at all energies, both the cross sections and the analyzing powers.
           
The results confirm the large effect of the (knock-out) exchange amplitudes in the elastic scattering process and which make the coordinate space optical potentials nonlocal. In almost all past coordinate space studies of pA elastic scattering, be they with a Schrodinger, Dirac or relativistic impulse approximation formulation, inherent  exchange amplitudes either have been ignored or localized.
           
Although the predictions of the scattering are good at all energies they are better for energies below pion threshold than above. Notably at energies above pion threshold, my   best results for the forward scattering angle analyzing powers overpredict the data. This may be due to the treatment of pion production and resonance effects being too simplistic and not providing pertinent off-shell properties of the NN t- and g matrices at those energies to specify the appropriate details of the effective interactions. Nevertheless to analyze the Helium isotopes, I have used the BCC3 boson exchange model NN interaction modulated by NN optical potentials with which the SM97 NN scattering phase shifts to 2.5 GeV were reproduced to specify NN t- and g-matrices at 800 MeV. Coordinate space effective interaction forms that map those t- and g-matrices have been determined and then used in a g-folding process to specify a complex and nonlocal optical potential for 800 MeV protons incident on 3,4He. The structure of the target used in that folding was determined from a large space shell model calculation; the ground state wave function of which leads to an electron scattering longitudinal form factor in good agreement with measured values. Thereby all quantities required in the folding process were preset to make solution of the associated nonlocal p-3,4He Schrodinger equations predictive of the scattering phase shifts, and so of the differential cross sections and spin transfer observables. The predicted results agree very well with the observation for momentum transfer values to that at which the cross section is of the order of 0.1 mb/sr.
           
The cross section and analyzing power results obtained from the coordinate space nonlocal optical potentials formed by g folding at 25, 30, and 40 MeV are in quite reasonable agreement with the data obtained with targets of mass 6 to 238; the 40 MeV results the more so. In general the cross section predictions give the magnitudes and trends of the peaks in the data but the minima are too sharply defined.  The comparisons between the calculated results and the data for 25 and 30 MeV proton elastic scattering remain reasonable but the disparities are more pronounced than at higher energies. Nevertheless, the g folding optical potentials remain a reasonable first approximation, sufficiently so that the results may still select between different structure inputs. Also the associated distorted wave functions and effective interactions still should be appropriate for use in DWA analyses of inelastic scattering from stable nuclei, or of radioactive beam ions, as well as of other reaction calculations.
           
The scattering of 65 to 300 MeV protons from nuclei remain as the best set with which the g-folding optical potentials give matches to data. Those data then can be used in analyses to select between diverse options for the nucleonic based structure of the target nucleus. I have shown how that is possible with analyses of nucleon scattering from 208Pb for which I had spectroscopy from a Skyrme-Hartree-Fock description of the nucleus to compare with what is usually used, a simple packed shell model representation. A clear preference was noted for use of the SHF prescription with both magnitudes and shapes of angular distributions. Of note was the sensitivity of proton scattering to the neutron matter distribution in 208Pb.
           
Finally I have used the microscopic model of nucleon-nucleus optical potential to predict successfully the total reaction cross sections. As with the predictions of the angular dependent observables, for optimum results for the light masses in particular it is essential to use the best (nucleon based) model specification of nuclear structure available. Marked improvement in results were obtained when, for 9Be and 12C in this study, complete shell model calculations were used to define the OBDME required in the folding processes. Of most significance however is the use of medium modified effective interactions for predictions to compare well with measured values of the integral observables. Of note are the variations of the partial reaction cross sections with mass and energy. They follow very well a simple, three parameter, and functional form. Those parameters have values that vary smoothly with mass and/or energy suggesting that the total and total reaction cross sections at energies, and perhaps for target mass, that have not been measured as yet, may be estimated with some confidence.

    
References

1.        M. B. Chadwick, Nuclear Data for Neutron and Proton Radiotherapy and for Radiation Protection. ICRU Report, 2000. 63.
2.         M. Kamran, Physics Report, 1984. 10: p. 275.
3.         H. Bethe, Physical Review, 1940. 57: p. 1125.
4.         C. M. Perey  and F. Perey, Atom. Data and Nucl. Data Tables 1974. 13: p. 293.
5.         G. R. Satchler, ed. Direct Nuclear Reactions, International series of monographs on physics. Vol. 68. 1983, Clarendon: New York.
6.         H. Feshbach, Theoretical Nuclear Physics: Nuclear Reactions. 1992, London: Wiley.
7.         K. Amos, et al., Adv. in Nucl. Phys. , 2000. 25: p. 275.
8.         P. E. Hodgson, The Nucleon Optical Model    1994, Singapore: World Scientific.
9.         E. Bauge, J. P. Delaroche, and M. Girod, Physical Review C, 1998. 58: p. 1118.
10.       F. Chew, Physical Review, 1951. 80: p. 196 
11.       K. M. Watson, Physical Review, 1953. 89: p. 575 
12.       N. Francis and K. M. Watson, Physical Review, 1953. 92: p. 291
13.       H. Bethe, Ann. Phys. , 1958. 3: p. 190
14.       A. K. Kerman, H. McManus, and R. M. Thaler, Ann. Phys. (N.Y.), 1959. 8: p. 551 
15.    S. K. Adhikari and K. L. Kowalski, in Dynamical Collision Theory and its Applications. 1991, Academic Press: New York.
16.       R. A. Arndt, I. I. Strakovsky, and R. L. Workman, Physical Review C, 1994. 50: p. 2731
17.       R. A. Arndt, et al., Physical Review C, 1997. 56: p. 3005
18.       R. A. Arndt, Physical Review D, 1983. 28: p. 97.
19.       M. M. Nagels, T. A. Rijken, and J. J. de Swart, Physical Review D, 1978. 17: p. 768
20.       M. Lacombe, Physical Review C, 1980. 21: p. 861 
21.       R. Machleidt, K. Holinde, and C. Elster, Physics Report, 1987. 149: p. 1.
22.       H. V. von Geramb. Microscopic Optical Potentials. in Hamburg Topical Workshop. 1979. Berlin: Springer-Verlag.
23.       P. Schwandt, Proc. Int. Workshop on Medium Energy Nucleons in Nuclei, in AIP Conf. Proc 97, H.O. Meyer, Editor. 1983, AIP: New York.
24.       L. Ray, Physical Review C, 1990. 41: p. 2816 
25.       A. A. Korsheninnikov, Nuclear Physics, 1997. A617: p. 45
26.       R. W. Manweiler, Nuclear Physics, 1975. A240: p. 373
27.       K. Nakayama, et al., Nuclear Physics, 1984. A431: p. 419
28.       F. Brieva, H. V. von Geramb, and R. Rook, Physics Letters, 1978. 79B: p. 177 
29.       W. G. Love and M. A. Franey, Physical Review C, 1981. 24: p. 1073 
30.       J. Raynal, computer code DWBA91, in NEA 1209/02 1991.
31.       J. Raynal, computer code DWBA98, in NEA 1209/05 1999.
32.       V. G. J. Stokes, et al., Physical Review C, 1994. 49: p. 2950
33.       R. Machleidt, Adv. in Nucl. Phys., 1989. 19: p. 189 
34.       R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Physical Review C, 1995. 51: p. 38
35.       L. Jade and H. V. von Geramb, Physical Review C, 1998. 57: p. 496 
36.       C. Elster, Physical Review C, 1988. 37: p. 1647.
37.       C. Elster, Physical Review C, 1988. 38: p. 1828
38.       L. Ray, Physical Review C, 1987. 35: p. 1072
39.       H. Feshbach, Ann. Phys. (N.Y.) 1958. 5: p. 357.
40.       H. Feshbach, Ann. Phys. (N.Y.) 1962. 19: p. 287 
41.       H. V. von Geramb and K. Nakano. in Workshop on the Interaction Between Medium Energy Nucleons in Nuclei. 1983: AIP.
42.       H. V. von Geramb, et al., Physical Review C, 1991. 44: p. 73 
43.       K. A. Brueckner, C. A. Levinson, and H. M. Marmoud, Physical Review, 1954. 95: p. 217.
44.       K. A. Brueckner and C. A. Levinson, Physical Review, 1955. 97: p. 1344 
45.       H. A. Bethe, B. H. Brandow, and A. G. Petschek, Physical Review, 1963. 129: p. 225.
46.       B. A. Lippmann and J. Schwinger, Physical Review, 1950. 79: p. 669 
47.       H. Bethe, Physical Review, 1968. 167: p. 879 
48.       H. J. Yuan, et al., physical Review c, 1989. 40: p. 1448.
49.       T. Cheon, Physical Review C, 1988. 38: p. 1516 
50.       K. H. Muller, Z. Phys. , 1980. A295: p. 79 
51.       E. F. Redish, J. G. Stephenson, and G. M. Lerner, Physical Review C, 1970. 2: p. 1665.
52.       E. F. Redish and K. Stricker-Bauer, Physical Review C, 1987. 35: p. 1183 
53.       K. Amos, et al., Nuclear Physics, 1988. A499: p. 45.
54.       T. Kirst, Physical Review C, 1989. 40: p. 912 
55.       B. Sinha, Physical Review C, 1975. 20: p. 1.
56.       H. F. Arellano, F. A. Brieva, and W. G. Love, Physical Review C, 1990. 41: p. 2188.
57.       C. Elster, et al., Physical Review C, 1990. 41: p. 814.
58.       H. F. Arellano, F. A. Brieva, and W. G. Love, Physical Review C, 1995. 52: p. 301.
59.       C. R. Chinn, et al., Physical Review C, 1995. 52: p. 1992 
60.       P. J. Dortmans and K. Amos, Journal of Physics G, 1991. 17: p. 901 
61.       M. Haftel and F. Tabakin, Nuclear Physics, 1970. A158: p. 1 
62.       W. Legindgaard, Nuclear Physics, 1978. A297: p. 429 
63.       T. Cheon and E. F. Redish, Physical Review C, 1989. 39: p. 331 
64.       H. A. Bethe, Physical Review, 1956. 103: p. 1353 
65.       K. A. Brueckner and J. L. Gammel, Physical Review, 1958. 109: p. 1023 
66.       K. Amos, Physical Review C, 1988. 37: p. 934 
67.       J. P. Jeukenne, A. Lejeunne, and C. Mahaux, Physics Report, 1976. 25: p. 83 
68.       C. Mahaux, Nuclear Physics, 1979. A328: p. 24 
69.       J. Hufner and C. Mahaux, Ann. Phys. (N.Y.), 1972. 73: p. 525 
70.       H. P. Noyes, Physical Review Letters, 1965. 15: p. 538 
71.       K. L. Kowalski, Physical Review Letters, 1965. 15: p. 798 
72.       P. J. Dortmans and K. Amos, Physical Review C, 1993. 48: p. 2112 
73.       L. Jade and H. V. von Geramb, Physical Review C, 1997. 55: p. 57 
74.       P. J. Dortmans, K. Amos, and S. Karataglidis, Physical Review C, 1998. 57: p. 2433.
75.       P. J. Dortmans, K. Amos, and S. Karataglidis, Journal of Physics G, 1997. 23: p. 183.
76.       P. K. Deb and K. Amos, Physical Review C, 2000. 62: p. 024605
77.       P. K. Deb, K. Amos, and S. Karataglidis, Physical Review C, 2000. 62: p. 037601
78.       P. K. Deb, K. Amos, and S. Karataglidis, Australian Journal of Physics, 2001. 53: p. 767.
79.       R. V. Reid, Ann. Phys. (N.Y.), 1968. 50: p. 411 
80.       M. A. Franey and W. G. Love, Physical Review C, 1985. 31: p. 488 
81.       H. V. von Geramb, et al., Physical Review C, 1998. 58: p. 1948
82.       L. Wolfenstein, Ann. Rev. of Nucl. Sci. , 1956. 6: p. 43 
83.       L. Allen, K. Amos, and P. J. Dortmans, Physical Review C, 1994. 49: p. 2177
84.       S. G. Cooper and R. S. Mackintosh, Physical Review C, 1996. 54: p. 3133
85.       H. F. Arellano, et al., Physical Review C, 1996. 54: p. 2570 
86.       C. Elster, S. P. Weppner, and C. R. Chinn, Physical Review C, 1997. 56: p. 2080.
87.       S. Karataglidis, et al., Physical Review C, 1995. 52: p. 861 
88.       P. J. Dortmans, et al., Physical Review C, 1998. 58: p. 2249 
89.       J. J. Kelly and S. J. Wallace, Physical Review C, 1994. 49: p. 1315
90.       S. Cohen and D. Kurath, Nuclear Physics, 1965. 73: p. 1.
91.       D. J. Millener and D. Kurath, Nuclear Physics, 1975. A255: p. 315
92.       S. Karataglidis, et al., Australian Journal of Physics, 1996. 49: p. 644 
93.       P. J. Dortmans and K. Amos, Physical Review C, 1994. 49: p. 1309 
94.       R. Machleidt and G.Q. Li, Physics Report, 1994. 242: p. 5.
95.       L. Jade, Physical Review C, 1998. 58: p. 96 
96.       A. Bulla and P.U. Sauer, Few Body Systems 1992. 12: p. 141
97.       L. N. Blumberg, et al., Physical Review, 1966. 147: p. 812
98.       J. A. Fannon, et al., Nuclear Physics, 1967. A97: p. 263
99.       S. Kato, Physical Review C, 1985. 31: p. 1616
100.     J. R. Comfort, Physical Review C, 1981. 24: p. 1834
101.     W. Bauhoff, Nuclear Physics, 1983. A410: p. 180 
102.     J. M. Dickson and D. C. Salter, Nuovo Cim. , 1957. 6: p. 235
103.     O. N. Jarvis, C. Whitehead, and M. Shah, Nuclear Physics, 1972. A184: p. 615
104.     V. Comparat, PhD thesis,. 1975 Centre d'Orsay, Universite Paris-Sud,.
105.     H. O. Meyer, et al., Physical Review C, 1983. 27: p. 459 
106.     A. Ingermarsson, O. Jonsson, and A. Hallgren, Nuclear Physics, 1979. A319: p. 377
107.     J. R. Comfort, et al., Physical Review C, 1982. 26: p. 1800
108.     H. Togawa, RCNP annual report, 1985: p. 1.
109.     H. O. Meyer, Physical Review C, 1985. 31: p. 1569
110.     H. Sakaguchi, in R.C.N.P. annual report, . 1993. p. 4.
111.     F. T. Baker, Physical Review C, 1993. 48: p. 1106
112.     K. W. Jones, Physical Review C, 1994. 50: p. 1982 
113.     K. W. Jones, Physics Letters, 1983. 128B: p. 281 
114.     K. W. Jones, Physical Review C, 1986. 33: p. 17
115.     G. W. Hoffmann, Physical Review C, 1980. 41: p. 1651
116.     G. S. Blanpied, C. Shekhar Mishra, and B. G. Ritchie, Physical Review C, 1986. 33: p. 1527
117.     P. J. Dortmans, et al., Physical Review C, 1995. 52: p. 3224
118.     F. Auger. in Conference on Experimental Nuclear Physics in Europe ENPE '99. 1999. Seville, Spain.
119.     A. C. Mueller, Nuclear Physics, 1999. A654: p. 215c
120.     I. Tanihata, Nuclear Physics, 1999. A654: p. 235c
121.     A. Lagoyannis, Physics Letters, 2001. B518: p. 27-33.
122.     H. V. von Geramb, et al., Physical Review C, 1975. 12: p. 1697
123.     S. Karataglidis, et al., Physical Review C, 1997. 55: p. 2826 
124.     P. J. Dortmans, K. Amos, and S. Karataglidis, Physical Review C, 1997. 55: p. 2723.
125.     B. A. Mughrabi, et al., Physical Review C, 1984. 29: p. 29
126.     F. Petrovich, et al., Nuclear Physics, 1993. A563: p. 387
127.     K. T. Knopfle, et al., in Julich-Report. 1973.
128.     H. F. Lutz, D. W. Heikkinen, and W. Bartolini, Nuclear Physics, 1972. A198: p. 257
129.     J. L. Escudie', et al., Physical Review C, 1974. 10: p. 1645
130.     R. Roy, et al., Nuclear Physics, 1983. A411: p. 1.
131.     Roger Dittman, et al., Nuclear Physics, 1969. A126: p. 592
132.     C. R. Lamontagne, et al., Physics Letters, 1973. 45B: p. 465
133.     R. H. McCamis, Physical Review C, 1986. 33: p. 1624 
134.     S. D. Wassenaar, et al., Journal of Physics G, 1989. 15: p. 181.
135.     S. Austin, Private Communication, 2001.
136.     R. A. Moyer, R. W. Finlay, and G. M. Crawley, Nuclear Physics, 1981. A352: p. 221
137.     M. P. Barbier, et al., Physics Letters, 1971. 34B: p. 386
138.     L. F. Hansen, et al., Physical Review C, 1982. 25: p. 189
139.     R. M. Craig, Nuclear Physics, 1964. 58: p. 515
140.     A. Tarratis, J. L. Esudie, and I. Brissaud, Nuclear Physics, 1981. A362: p. 128
141.     H. J. Votava, et al., Nuclear Physics, 1973. A204: p. 529
142.     D. L. Pham and R. De Swiniarski, Nuovo Cim., 1977. 41A: p. 543
143.     P. D. Greaves, et al., Nuclear Physics, 1972. A179: p. 1.
144.     A. A. Rush, E. J. Burge, and D. A. Smith, Nuclear Physics, 1971. A166: p. 378
145.     G. L. Thomas, E. J. Burge, and D. A. Smith, Nuclear Physics, 1971. A171: p. 165
146.     B. W. Ridley and J. F. Turner, Nuclear Physics, 1964. A58: p. 497
147.     D. J. Baugh, et al., Nuclear Physics, 1967. A99: p. 203
148.     W. H. Tait, E. J. Burge, and V. R. W. Edwards, Nuclear Physics, 1971. A176: p. 390
149.     R. de Swiniarski, Dinh-Lien Pham, and G. Bagieu, Canadian Journal of Physics, 1977. 55: p. 43
150.     G. P. A. Berg, Nuclear Physics, 1982. A379: p. 93
151.     A. G. Hardacre, et al., Nuclear Physics, 1971. A173: p. 436
152.     V. D. Helten, J. C. Hilbert, and J. B. Ball, Nuclear Physics, 1973. A201: p. 225
153.     O. Kamigaito, in RCNP Annual Report. 1988.
154.     H. S. Sandhu, Nuclear Physics, 1970. A146: p. 163
155.     V.Hnizdo, et al., Physical Review C, 1971. 3: p. 1560
156.     B. C. Sinha, et al., Nuclear Physics, 1972. A183: p. 401
157.     K. H. Bray, Nuclear Physics, 1972. A189: p. 35
158.     L. Zuffi, G. Maino, and A. Ventura, Physical Review C, 1986. 34: p. 1223
159.     H. S. Sandhu, J. M. Cameron, and W. F. Mcgill, Nuclear Physics, 1971. A169: p. 600
160.     J. L. Snelgrove and E. Kashy, Physical Review, 1969. 187: p. 1259
161.     J. P. Delaroche, M. S. Islam, and R. W. Finlay, Physical Review C, 1986. 33: p. 1826
162.     H. S. Liers, et al., Physical Review C, 1970. 2: p. 1399
163.     R. de Swiniarski, et al., Canadian Journal of Physics, 1979. 57: p. 540
164.     Richard N. Boyd and G. W. Greenlees, Physical Review, 1968. 176: p. 1394
165.     B. L. Berman, Atom. Data and Nucl. Data Tables, 1975. 15: p. 319
166.     W. A. Richter, Physical Review C, 1996. 54: p. 1756
167.     J. L. Friar, B. F. Gibson, and G. L. Payne, Ann. Rev. Nucl. Part. Sci., 1984. 34: p. 403
168.     P. Navratil and B. R. Barrett, Physical Review C, 1998. 57: p. 3119 
169.     M. Geso, et al., Physical Review C, 2002. 65: p. 034005.
170.     P. Navratil and B. R. Barrett, Physical Review C, 1998. 57: p. 3119
171.     D. C. Zheng, et al., Physical Review C, 1995. 52: p. 2488
172.     A Etchegoyen, et al., OXBASH-MSU (the Oxford- Buenos- Aries- Michigan State University shell model code), , B. A. Brown, Editor. 1986
173.     D. R. Tilley, H. R. Weller, and H. H. Hansen, Nuclear Physics, 1987. A474: p. 1.
174.     D. R. Tilley, H. R. Weller, and G. M. Hale, Nuclear Physics, 1992. A541: p. 1.
175.     W. Glockle, et al., Few Body Systems Suppl., 1995. 8: p. 9.
176.     H. Courant, Physical Review C, 1979. 19: p. 104
177.     M. Geso, Physical Review C, 1998. 58: p. 3742
178.     I. Tanihata. in Proceedings of INPC. 1995. Beijing.
179.     S. Karataglidis, et al., Physical Review C, 2000. 61: p. 024319
180.     P. Navratil and B. R. Barrett, Physical Review C, 1996. 54: p. 2986 
181.     S. P. Weppner, Ofir Garcia, and Ch. Elster, Physical Review C, 2000. 61: p. 044601.
182.     D. Gupta, C. Samanta, and R. Kanungo, Nuclear Physics, 2000. A674: p. 77
183.     B. Abu-Ibrahim, K. Fujimura, and Y. Suzuki, Nuclear Physics, 1999. A657: p. 391
184.     S. Karataglidis, et al., Physical Review C, 1996. 53: p. 838
185.     F. Ajzenberg-Selove, Nuclear Physics, 1988. A490: p. 1.
186.     D. J. Plummer, et al., Nuclear Physics, 1971. A174: p. 193
187.     S. M. Bunch, H. H. Forster, and C. C. Kim, Nuclear Physics, 1964. 53: p. 241.
188.     A. D. Bacher, Physical Review C, 1972. 5: p. 1147
189.     O. G. Grebenjun, Nuclear Physics, 1989. A500: p. 637
190.     G. D. Alkhazov, Physical Review Letters, 1997. 78: p. 2313
191.     D. D. Bogdanov and G. Lobo, Private Communication, 2001.
192.     G. Fricke, Atom. Data and Nucl. Data Tables, 1995. 60: p. 177.
193.     L. Ray, G. W. Hoffmann, and W. R. Coker, Physics Report, 1992. 212: p. 223.
194.     B. A. Brown, Physical Review Letters, 2000. 85: p. 5296
195.     C. W. Glover, IUCF Scientific and Technical Report, 1982: p. 7.
196.     R. N. Boyd and G. W. Greenlees, Physical Review, 1968. 176: p. 1394.
197.     P. Kirkby and W. T. Link, Canadian Journal of Physics, 1966. 44: p. 1847
198.     G. P. Millburn, et al., Physical Review, 1954. 95: p. 1268
199.     B. D. Wilkins and G. Igo, Physical Review, 1963. 129: p. 2198
200.     J. J. H. Menet, et al., Physical Review C, 1971. 4: p. 1114
201.     R. Goloskie and K. Strauch, Nuclear Physics, 1962. 29: p. 474.
202.     R. F. Carlson, Physical Review C, 1975. 12: p. 1167
203.     H. Sakaguchi, et al., Physical Review C, 1982. 26: p. 944.
204.     A. Nadasen, PhD Thesis. 1977, Indiana University, : Bloomington, Indiana 47401,.
205.     D. A. Hutcheon, Nuclear Physics, 1988. A483: p. 429.
206.     D. A. Hutcheon. in Polarization Phenomena in Nuclear Physics - Fifth International Symposium. 1980 Santa Fe: AIP, New York, .
207.     O. Hausser, Physics Letters, 1987. B184: p. 316.
208.     B. Aas, Nuclear Physics, 1986. A460: p. 675
209.     A. M. Mack, Physical Review C, 1995. 52: p. 291.
210.     G.W. Hoffmann, Physical Review C, 1981. 24: p. 541.
211.     R.W.Fergerson, Physical Review C, 1986. 33: p. 239.
212.     P. K. Deb, et al., Physical Review Letters, 2001. 86: p. 3248 
213.     W. Wlazlo, Physical Review Letters, 2000. 84: p. 5736
214.     X. Ledoux, Physical Review Letters, 1999. 82: p. 4412
215.     R. F. Carlson, Atom. Data and Nucl. Data Tables, 1996. 63: p. 93.
216.     A. Johansson, U. Svanberg, and O. Sundberg, Arkiv Fysik 1961. 19: p. 527
217.     A. Ingemarsson, Nuclear Physics, 1999. A653: p. 341
218.     W. F. McGill, Physical Review C, 1974. 10: p. 2237
219.     D. G. Montague, et al., Nuclear Physics, 1973. A199: p. 457
220.     P. U. Renberg, et al., Nuclear Physics, 1972. A183: p. 81.
221.     I. Slaus, et al., Physical Review C, 1975. 12: p. 1093
222.     M. Q. Makino, C. N. Waddell, and R. M. Eisberg, Nuclear Physics, 1965. 68: p. 378
223.     E. J. Burge, Nuclear Physics, 1959. 13: p. 511.
224.     J. M. Cassels and J. D. Lawson, Proc. Phys. Soc., London, , 1954. A67: p. 125.
225.     R. A. Giles and E. J. Burge, Nuclear Physics, 1964. 50: p. 327.
226.     M. Q. Makino, C. N. Waddell, and R. M. Eisberg, Nuclear Physics, 1964. 50: p. 145.
227.     T. J. Gooding, Nuclear Physics, 1959. 12: p. 241.
228.     V. Meyer, R. M. Eisberg, and R. F. Carlson, Physical Review, 1960. 117: p. 1334
229.     R. Chapman and A. M. Macleod, Nuclear Physics, 1967. A94: p. 313
230.     K. Bearpark, W. R. Graham, and G. Jones, Nuclear Physics, 1965. 73: p. 206
231.     V. Meyer and N. M. Hintz, Physical Review Letters, 1960. 5: p. 207.
232.     R. E. Pollock and G. Schrank, Physical Review, 1965. 140: p. B575.
233.     J. F. Dicello and G. Igo, Physical Review C, 1970. 2: p. 488.
234.     J. F. Turner, et al., Nuclear Physics, 1964. 58: p. 509.
235.     R. D. Albert and L.F. Hansen, Physical Review Letters, 1961. 6: p. 13.
236.     J. F. Dicello, G. J. Igo, and M. L. Roush, Physical Review, 1967. 157: p. 1001.
237.     C. Hojvat and G. Jones, Nucl. Instrum. Methods 1968. 66: p. 13.
238.     M. Q. Makino, et al., Physics Letters, 1964. 9: p. 178.
239.     R. F. Carlson, et al., Canadian Journal of Physics, 1995. 73: p. 512.
240.     N. E. Davison, Nuclear Physics, 1977. A290: p. 45.
241.     R. Abegg, Nuclear Physics, 1979. A324: p. 109
242.     J. W. Wilson, Transport methods and interaction for space radiations. NASA Reference Publications, 1991: p. 1257.
243.     S. Karataglidis, et al., Physical Review C, 2002. 65: p. 044306.
244.     K. Amos, S. Karataglidis, and P. K. Deb, Physical Review C, 2002. 65: p. 064618.
245.     A. J. Koning and J. P. Delaroche, Nuclear Physics, 2003. A713: p. 231.
246.     K. Amos and P. K. Deb, Physical Review C, 2002. 66: p. 024604.
247.     P. K. Deb and K. Amos, Physical Review C, 2003. 67: p. 067602.
248.     H. von Geramb, et al., Physical Review C, 1998. 58: p. 2249.
249.     W. P. Abfalterer, et al., Physical Review C, 2001. 63: p. 044608.
250.     R. W. Finlay, et al., Physical Review C, 1993. 47: p. 237.


Latest Post

Young Scientist Gitanjali Rao

At just twelve years old and in seventh grade, Gitanjali Rao earned the title of America’s Top Young Scientist in 2017 after developing &quo...

Popular Posts