Three-body radiative capture reactions in astrophysics L.V. Grigorenko K.-H. Langanke and M. Zhukov FLNR, JINR, Dubna and GSI, Darmstadt

Modes of two-proton radiative capture  rp-process at high temperature and density.  15 O, 18 Ne, 38 Ca : J.Görres, M.Wiescher, and F.-K.Thielemann, PRC 51 (1995) 392.  68 Se, 72 Kr, …, 96 Cd : H.Schatz et al., Phys. Rep. 294 (1998) 167.  Could be important in the regions of nuclear chart, where there are “ridges” connected with paring and intermediate system is not nuclear stable.  Analogy with true 2p emission.

Conventional approach  The capture rate do not depend on number and properties of the intermediate states. Only on the sum of widths to these states. Paradox if we consider situation without intermediate states.  Typical situation: and the reaction rate depends only on gamma width.  Problem: if the production rate decrease.  K. Nomoto, F. Thielemann, and S. Miyaji, Astron. Astrophys. 149 (1985) 239.  Introduced to study nonresonant capture. We consider only resonant part

Direct resonant two-proton capture  All the states should be taken into account in the final nucleus, not only those accessible by a sequence of binary captures  This equation reflects nothing more than current conservation complete thermal equilibrium and a detailed balance  Typical situation: and hence the reaction rate depends only on gamma width.  If the true 2p decay is the only decay branch of the state, and the reaction rate depends only on gamma width. need to know the reaction rate depends only on 2p width.  2p  L. Grigorenko, M. Zhukov, PRC 72 (2005)  S-matrix formalism for 3→3 scattering

Theory of two-proton radioactivity Classical case: one particle emission is always possible Quantum mechanical case: it could be that both particles should be emitted simultaneously  2p radioactivity (“true” 2p decay) suggested in : V.I. Goldansky, NP 19 (1960) 482  Coulomb three-body problem in continuum is intractable in general case  First consistent quantum mechanical treatment of 2p radioactivity :  L. V. Grigorenko, et al., PRL 85 (2000) 22.  L. V. Grigorenko, et al., PRC 64 (2001)  L. V. Grigorenko, M. V. Zhukov, PRC 68 (2003)  Subject : 6 Be, 8 Li *, 12 O, 16 Ne, 17 Ne *, 19 Mg, 30 Ar, 34 Ca, 45 Fe, 48 Ni, 54 Zn, 58 Ge, 62 Se, 66 Kr

Recent status of 2p decay studies  2p radioactivity suggested: 1960  Discovery of 2p radioactivity: 2002  45 Fe : M. Pfutzner, et al., EPJA 14 (2002) 279.  54 Zn : B. Blank, et al., PRL 94 (2005)  48 Ni : B. Blank, et al., PRC 72 (2005)  Planned research:  45 Fe correlations (MSU)  19 Mg (GSI)

Practical application to 2p capture  Waiting points of r-p process: 15 O, 18 Ne, and 38 Ca.  T 1/2 for β + decay : 122 s, 1.67 s, and 0.44 s.  Possibility to bridge the waiting points by 2p capture: J. Görres, M. Wiescher, and F.-K. Thielemann, Phys. Rev. C 51 (1995) 392.  Only sequential processes taken into account.  15 O(2p,  ) 17 Ne omitted: 3/2  state at 1288 keV (Q 2p =344 keV)  18 Ne(2p,  ) 20 Mg  38 Ca(2p,  ) 40 Ti omitted: 0  state at 2100 keV (Q 2p = keV)

Direct nonresonant two-proton capture  Single particle 1 - states are highly excited, low-lying 1 - states are complicated particle- hole excitations. Thus low-lying 1 - states have small B E1 values.  In conventional approach the dB E1 (E)/dE values are considered as transitions to “wings” of known low-lying states (having small B E1 values) or GDR. Thus they are small.  The nonresonant E1 exhaust large part of the cluster sum rule just above Coulomb barrier independently on the details of spectrum of narrow states.  For calculations in the Gamow peak region the simplified three-body model with only one FSI is applied.  L. Grigorenko, K.-H. Langanke, M. Zhukov, preliminary.  Domination of the E1 process (e.g. E2 is “exosted” by resonant capture)

“Soft E1” mode in proton dripline nuclei  Existence of “soft E1” mode now established in neutron-rich nuclei.  Cluster sum rule exhausted within several MeV above 2p threshold.  Possibility of “soft E1” in proton-dripline nuclei.  Calculations predict a strong and narrow E1 peak in 17 Ne.  The 2p capture rate is dominated by the nonresonant E1 for T 0.4  1.0 GK

Conclusion  We found that for resonant two-proton radiative capture all the states should be taken into account in the final nucleus, not only those accessible by a sequence of binary captures.  The widhts of the states - “true” two-proton emitters (those having no sequential decay path) are calculated within quantum mechanical three-body model tested on a variety of three-body decays.  For nonresonant two-proton radiative capture the contribution of E1 transition directly from continuum can be large. E.g. in 17 Ne this transition dominates the 2p capture rate practically in the whole temperature range.  The importance of this class of phenomena in the heavier nuclei, which are rp-process waiting points to be understood.