Abstract.
Odd-even effects, also known as staggering effects, are a common feature observed in the yield distributions of fragments produced in different types of nuclear reactions. We review old methods, and we propose new ones, for a quantitative estimation of these effects as a function of proton or neutron number of the reaction products. All methods are compared on the basis of Monte Carlo simulations. We find that some are not well suited for the task, the most reliable ones being those based either on a non-linear fit with a properly oscillating function or on a third (or fourth) finite difference approach. In any case, high statistic is of paramount importance to avoid that spurious structures appear just because of statistical fluctuations in the data and of strong correlations among the yields of neighboring fragments.
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N.G. Runnalls, D.E. Troutner, Robert L. Ferguson, Phys. Rev. 179, 1188 (1969)
B.L. Tracy, J. Chaumont, R. Klapisch, J.M. Nitschke, A.M. Poskanzer, E. Roeckl, C. Thibault, Phys. Rev. C 5, 222 (1972)
H.-G. Clerc, W. Lang, H. Wohlfarth, K.-H. Schmidt, H. Schrader, K.E. Pferdekämper, R. Jungmann, Z. Phys. A 274, 203 (1975)
G. Siegert, H. Wollnik, J. Greif, R. Decker, G. Fiedler, B. Pfeiffer, Phys. Rev. C 14, 1864 (1976)
I. Tsekhanovich, H.O. Denschlag, M. Davi, Z. Büyükmumcu, M. Wöstheinrich, F. Gönnenwein, S. Oberstedt, H.R. Faust, Nucl. Phys. A 658, 217 (1999)
K.-H. Schmidt, J. Benlliure, A.R. Junghans, Nucl. Phys. A 693, 169 (2001)
I. Tsekhanovich, N. Varapai, V. Rubchenya, D. Rochman, G.S. Simpson, V. Sokolov, G. Fioni, Ilham Al Mahamid, Phys. Rev. C 70, 044610 (2004)
H. Naik, S.P. Dange, A.V.R. Reddy, Nucl. Phys. A 781, 1 (2007)
F. Rejmund, A.V. Ignatyuk, A.R. Junghans, K.-H. Schmidt, Nucl. Phys. A 678, 215 (2000)
A.C. Wahl, R.L. Ferguson, D.R. Nethaway, D.E. Troutner, K. Wolfsberg, Phys. Rev. 126, 1112 (1962)
F. Gönnenwein, Nucl. Instrum. Methods A 316, 405 (1992)
S. Amiel, H. Feldstein, in Third International Symposium on Physics and Chemistry of Fission, Vol. II (IAEA, Vienna, 1974) p. 65
S. Amiel, H. Feldstein, Phys. Rev. C 11, 845 (1975)
A.C. Wahl, J. Radioanal. Chem. 55, 111 (1980)
A.M. Poskanzer, G.W. Butler, E.K. Hyde, Phys. Rev. C 3, 882 (1971)
W.R. Webber, J.C. Kish, D.A. Schrier, Phys. Rev. C 41, 533 (1990)
C.N. Knott, S. Albergo, Z. Caccia, C.-X. Chen, S. Costa, H.J. Crawford, M. Cronqvist, J. Engelage, P. Ferrando, R. Fonte et al., Phys. Rev. C 53, 347 (1996)
C. Zeitlin, L. Heilbronn, J. Miller, S.E. Rademacher, T. Borak, T.R. Carter, K.A. Frankel, W. Schimmerling, C.E. Stronach, Phys. Rev. C 56, 388 (1997)
M.V. Ricciardi, A.V. Ignatyuk, A. Kelič, P. Napolitani, F. Rejmund, K.-H. Schmidt, O. Yordanov, Nucl. Phys. A 733, 299 (2004)
P. Napolitani, K.-H. Schmidt, L. Tassan-Got, P. Armbruster, T. Enqvist, A. Heinz, V. Henzl, D. Henzlova, A. Kelić, R. Pleskač et al., Phys. Rev. C 76, 064609 (2007)
P. Napolitani, K.-H. Schmidt, L. Tassan-Got, J. Phys. G 38, 115006 (2011)
L.B. Yang, E. Norbeck, W.A. Friedman, O. Bjarki, F.D. Ingram, R.A. Lacey, D.J. Magestro, M.L. Miller, A. Nadasen, R. Pak et al., Phys. Rev. C 60, 041602(R) (1999)
E.M. Winchester, J.A. Winger, R. Laforest, E. Martin, E. Ramakrishnan, D.J. Rowland, A. Ruangma, S.J. Yennello, G.D. Westfall, A. Vander Molen, E. Norbeck, Phys. Rev. C 63, 014601 (2000)
E. Geraci, M. Bruno, M. D’Agostino, E. De Filippo, A. Pagano, G. Vannini, M. Alderighi, A. Anzalone, L. Auditore et al., Nucl. Phys. A 732, 173 (2004)
M. D’Agostino, M. Bruno, F. Gulminelli, L. Morelli, G. Baiocco, L. Bardelli, S. Barlini, F. Cannata, G. Casini, E. Geraci et al., Nucl. Phys. A 861, 47 (2011)
G. Ademard, J.P. Wieleczko, J. Gomez del Campo, M. La Commara, E. Bonnet, M. Vigilante, A. Chbihi, J.D. Frankland, E. Rosato, G. Spadaccini et al., Phys. Rev. C 83, 054619 (2011)
I. Lombardo, C. Agodi, F. Amorini, A. Anzalone, L. Auditore, I. Berceanu, G. Cardella, S. Cavallaro, M.B. Chatterjee, E. De Filippo et al., Phys. Rev. C 84, 024613 (2011)
M. D’Agostino, M. Bruno, F. Gulminelli, L. Morelli, G. Baiocco, L. Bardelli, S. Barlini, F. Cannata, G. Casini, E. Geraci et al., Nucl. Phys. A 875, 139 (2012)
G. Casini, S. Piantelli, P.R. Maurenzig, A. Olmi, L. Bardelli, S. Barlini, M. Benelli, M. Bini, M. Calviani, P. Marini et al., Phys. Rev. C 86, 011602(R) (2012)
S. Piantelli, G. Casini, P.R. Maurenzig, A. Olmi, S. Barlini, M. Bini, S. Carboni, G. Pasquali, G. Poggi, A.A. Stefanini, S. Valdrè et al., Phys. Rev. C 88, 064607 (2013)
M. Colonna, F. Matera, Phys. Rev. C 71, 064605 (2005)
Ad.R. Raduta, F. Gulminelli, Phys. Rev. C 75, 044605 (2007)
M. Huang, Z. Chen, S. Kowalski, Y.G. Ma, R. Wada, T. Keutgen, K. Hagel, M. Barbui, A. Bonasera, C. Bottosso et al., Phys. Rev. C 81, 044620 (2010)
Jun Su, Feng-Shou Zhang, Bao-An Bian, Phys. Rev. C 83, 014608 (2011)
M.V. Ricciardi, K.-H. Schmidt, A. Kelic-Heil, P. Napolitani, arXiv:1007.0386v1 [nucl-ex] (2010)
B. Mei, H.S. Xu, X.L. Tu, Y.H. Zhang, Yu.A. Litvinov, K.-H. Schmidt, M. Wang, Z.Y. Sun, X.H. Zhou, Y.J. Yuan, M.V. Ricciardi, A. Kelic-Heil et al., Phys. Rev. C 89, 054612 (2014)
A.S. Jensen, P.G. Hansen, B. Jonson, Nucl. Phys. A 431, 393 (1984)
D. Hove, A.S. Jensen, K. Riisager, Phys. Rev. C 88, 064329 (2013)
G. Iancu, F. Flesch, W. Heinrich, Radiat. Meas. 39, 525 (2005)
J.X. Cheng, X. Jiang, S.W. Yan, D.H. Zhang, J. Phys. G 39, 055104 (2012)
F. James, MINUIT: Function Minimization and Error Analysis - Reference Manual, http://wwwasdoc.web cern.ch/wwwasdoc/minuit/minmain.html (2000)
M. Luescher, Comput. Phys. Commun. 79, 100 (1994)
G. Boole, A treatise on the calculus of finite differences (Cambridge University Press, New York, 2009) (Reproduction of the original edition published in 1860)
C. Jordan, Calculus of finite differences (Chelsea Publishing Comp., New York, 1950) Schaum’s Outlines
M.R. Spiegel, Calculus of finite differences and difference equations (McGraw-Hill, Inc., 1971)
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Olmi, A., Piantelli, S. Methods for a quantitative evaluation of odd-even staggering effects. Eur. Phys. J. A 51, 154 (2015). https://doi.org/10.1140/epja/i2015-15154-4
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DOI: https://doi.org/10.1140/epja/i2015-15154-4