aim  to compare our model predictions with the measured (Dubna and GSI) evaporation cross sections for the 48 Ca Pb reactions. Calculations of fusion-evaporation cross sections in the 48 Ca Pb and 48 Ca Pb reactions K. Siwek-Wilczyńska, I. Skwira- Chalot, J. Wilczyński Kazimierz 2005 in future  to predict cross sections for the synthesis of super-heavy nuclei in cold and hot fusion reactions.

A collision of two heavy nuclei Overcoming the interaction barrier Fission fusion CN „Fast fission” ER n n  (synthesis) =  (capture) × P(fusion) × P(survive)

For moderately heavy, asymmetric systems ( Z CN < 100 ) P(fusion) ≈ 1  (evaporation residue) ≈  (capture) × P(survive) ≈  (fusion) × P(survive) Kazimierz Results of calculations for two reactions: 16 O Pb and 12 C U. For these two systems we know: experimental evaporation-residue cross sections experimental fusion cross sections experimental fission barriers (saddle energies). P(survival)

N - number of cascades which end at the ground state of a given final nucleus N tot - the total number of generated deexcitation cascades. The deexcitation cascade is determined at each step by branching ratios The survival probability is calculated using the Monte Carlo method. where: j = fission, n, p, d, t, , etc.  tot is the sum of all partial decay widths, including fission.

Partial widths for emission of light particles – Weisskopf formula where: The fission width (transition state method), E*< 40 MeV Upper limit of the final-state excitation energy after emission of a particle i Upper limit of the thermal excitation energy at the saddle  i – cross section for the production of a compound nucleus in inverse process m i, s i, ε i - mass, spin and kinetic energy of the emitted particle ρ, ρ i – level densities of the parent and the daughter nucleus

The level density is calculated using the Fermi-gas-model formula included as proposed by Ignatyuk (A.V. Ignatyuk et al., Sov. J. Nucl. Phys. 29 (1975) 255) Shell effects where: U - excitation energy, Ed - damping parameter – shell correction energy, δ shell (g.s.) (Möller et al., At. Data Nucl. Data Tables 59 (1995) 185), δ shell (saddle)≈ 0 B s, B k ( W.D. Myers and W.J. Świątecki, Ann. Phys. 84 (1974) 186), (W. Reisdorf, Z. Phys. A. – Atoms and Nuclei 300 (1981) 227)

our calculations: diffused-barrier formula 2n 3n 4n 5n K.Siwek-Wilczyńska, I Skwira, J. Wilczyński Phys. Rev. C 72 (2005) Experimental evaporation–residue cross sections T. Sikeland et al., Phys. Rev. 169 (1968) 1000 Experimental fusion cross Sections T. Murakami et al. Phys. Rev. C 34 (1986) 1353 Experimental fusion cross sections Morton et al. Phys. Rev. C 60 (1999) Experimental evaporation–residue cross sections V.I. Zagrebaev et al., Phys. Rev. C 65 (2001)

A  2 fit to 48 experimental near-barrier fusion excitation functions in the range of 40 < Z CN < 98 allowed for the systematics of the three parameters B 0, w, R  (K. Siwek-Wilczyńska, J. Wilczyński Phys. Rev. C 69 (2004) ) How to predict capture cross section ? The „diffused-barrier formula” ( 3 parameters): W. Świątecki, K. Siwek-Wilczyńska, J. Wilczyński Acta Phys. Pol. B34(2003)2049; Phys. Rev. C 71 (2005) Formula derived assuming: Gaussian shape of the fusion barrier distribution Classical expression for σ fus (E,B)

data: σ fission Yu. Ts. Oganessian, private comunication º σ fission R. Bock et al., Nucl. Phys. A 388 (1992) 334 The same method used for superheavy nuclei  (synthesis) =  (capture) × P(fusion) × P(survive) Z = 102 experimental evaporation–residue cross sections for xn channels experimental symmetric and asymmetric fission (capture) cross sections σ (capture) ≈ σ fission

data : ● Yu.Ts. Oganessian et al., Phys. Rev C (2001) ● A.V. Belozerov et al., Eur. Phys. J A (2003) ● H.W. Gäggeler et al., Nucl. Phys. A c (1989) ● A.V. Yeremin et al., JINR Rapid Commun (1998) calculations: σ (capture)  P(survival) Z CN = 102

experimental data: ● Yu.Ts. Oganessian et al., Phys. Rev. C (2001) ● A.V. Belozerov et al., Eur. Phys. J. A (2003) calculations : σ (capture)  P(survival) Z CN = 102

Z CN = 104 data: ● F.P. Heßberger et al., Z. Phys. A359 (1997) 415 calculations: σ (capture)  P(survival)

◦ 1n ● 2n ◊ 3n ● σ(capture)  P(survival) ● data P(fusion) = σ exp. (synthesis)/( σ (capture)  P(survival))

Summary Standard statistical model calculations with shell effects in the level density accounted for by Ignatyuk formula, and zero shell energy at the saddle were used to calculate cross sections for 1n, 2n, 3n and 4n channels in 48 Ca Pb reactions. The fusion probabilities reflecting the dynamical hindrance can be deduced empirically from measured evaporation residue cross sections for xn channels. These results can be used for empirical verification of theoretical models of the fusion hindrance process.