1 / 14

K. Siwek-Wilczyńska, I. Skwira- Chalot, J. Wilczyński

Calculations of fusion-evaporation cross sections in the 48 Ca + 208 Pb and 48 Ca + 206 Pb reactions. K. Siwek-Wilczyńska, I. Skwira- Chalot, J. Wilczyński. Kazimierz 2005.

keely-robles
Télécharger la présentation

K. Siwek-Wilczyńska, I. Skwira- Chalot, J. Wilczyński

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Calculations of fusion-evaporation cross sections in the 48Ca + 208Pb and 48Ca +206Pb reactions K. Siwek-Wilczyńska, I. Skwira- Chalot, J. Wilczyński Kazimierz 2005 aimto compare our model predictions with the measured (Dubna and GSI) evaporationcross sections for the 48Ca + 204-208Pb reactions. in futureto predict cross sections for the synthesis of super- heavy nuclei in coldand hotfusion reactions.

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

  3. For moderately heavy, asymmetric systems ( ZCN< 100 ) • P(fusion) ≈ 1 • (evaporation residue) ≈ (capture)× P(survive) • ≈ (fusion)× P(survive) • Kazimierz 2004 - • Results of calculations for two reactions: • 16O + 208Pb and 12C + 236U. • For these two systems we know: • experimental evaporation-residue cross sections • experimental fusion cross sections • experimental fission barriers (saddle energies). • P(survival)

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

  5. Partial widths foremission of light particles – Weisskopf formula where: Upper limit of the final-state excitation energy after emission of a particle i i– crosssection for the production of a compound nucleus in inverse process mi, si, εi- mass, spin and kinetic energy of the emitted particle ρ, ρi –level densities of the parent and the daughter nucleus The fissionwidth (transition state method), E*< 40 MeV Upper limit of the thermal excitation energy at the saddle

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

  7. K.Siwek-Wilczyńska, I Skwira, J. Wilczyński Phys. Rev. C 72 (2005) 004600 our calculations: diffused-barrier formula 2n 3n 4n 5n Experimental fusion cross sections Morton et al. Phys. Rev. C60 (1999) 044608 Experimental fusion cross Sections T. Murakami et al. Phys. Rev. C 34 (1986) 1353 Experimental evaporation–residue cross sections V.I. Zagrebaev et al., Phys. Rev. C 65 (2001) 014607 Experimental evaporation–residuecross sections T. Sikeland et al., Phys. Rev. 169 (1968) 1000

  8. 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) 014602 • Formula derived assuming: • Gaussian shape of the fusion barrier distribution • Classical expression for σfus(E,B) A 2 fit to 48 experimental near-barrier fusion excitation functions in the range of 40 < ZCN< 98 allowed for the systematics of the three parametersB0, w, R (K. Siwek-Wilczyńska, J. Wilczyński Phys. Rev. C 69 (2004) 024611)

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

  10. ZCN = 102 data : ● Yu.Ts. Oganessian et al., Phys. Rev C64 054606 (2001) ● A.V. Belozerov et al., Eur. Phys. J A16 447 (2003) ● H.W. Gäggeler et al., Nucl. Phys. A502 561c (1989) ● A.V. Yeremin et al., JINR Rapid Commun. 6 21 (1998) calculations: σ(capture)  P(survival)

  11. ZCN = 102 experimental data: ● Yu.Ts. Oganessian et al., Phys. Rev. C64 054606 (2001) ● A.V. Belozerov et al., Eur. Phys. J. A16 447 (2003) calculations : σ(capture)P(survival)

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

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

  14. 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 48Ca + 204 - 208Pb 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.

More Related