Nuclear and Coulomb excitations of the pygmy dipole resonances

Size: px

Start display at page:

Download "Nuclear and Coulomb excitations of the pygmy dipole resonances"

Leslie Shaw
5 years ago
Views:

1 SPES Legnaro, 5-7 ovember uclear and oulomb excitations of the pygmy dipole resonances M. V. Andrés a), F. tara b), D. Gambacurta b), A. Vitturi c), E. G. Lanza b) a)departamento de FAM, Universidad de Sevilla, Spain b)dipartimento di Fisica, Università di tania and IF-tania, Italy c)dipartimento di Fisica, Università di Padova and IF-Padova, Italy

Introduced by A.M. Lane (Ann. Phys. 63 (97) 7). lled pygmy because its strength much smaller than.

2 Introduced by A.M. Lane (Ann. Phys. 63 (97) 7). lled pygmy because its strength much smaller than. Later there have been several studies, microscopic and macroscopic, to try to relate this strength with the presence of a neutron skin. RPA calculations with Skyrme interaction were employed to study the multipole response in neutron rich nuclei. The spectral distributions of such nuclei are much more fragmented than those for well bound systems. For the dipole mode, additional strength has been found below the normal giant resonance region F. tara, E.G. Lanza, M.A. agarajan, A. Vitturi, PA 64 (997) 86; PA 64 (997) 449 Experimentally they have been measured mainly by mean of oulomb excitation by various groups using the FRS-LAD setup at GSI using the RISIG setup at GSI with (γ,γ ) studies below the neutron separation threshold (Darmstadt) with (α,α γ) at KVI. P.Adrich et al. PRL 95 (5) 35 O.Wieland et al. PRL (9) 95 D.Savran et al. PRL (8) 35 J.Endres et al. PR 8 (9) 343

3 db(e) /de (e fm MeV - ) 4 Sn Sn 3 Sn As an example we show some calculations done with the Hartree-Fock plus RPA with SGII Skyrme effective interactions. As far as the neutrons number increases more strength is found at low energy Similar calculations have been done before with similar results. See for example: -D. Sarchi, P. F. Bortignon, G. olò (HF+RPA or HF-BS+QRPA), PLB 6 (7) 7; -. Paar, T. ikšič, D. Vretenar, P. Ring (RHB+RQRPA) PLB 66 (5) 88; -E. Litvinova, P. Ring, D. Vretenar (RRPA+P) PLB 647 (7) ; -. Tsoneva and H. Lenske (QRPA+QPM) PR 77 (8) 43 See also the review paper -. Paar, D. Vretenar, E. Khan and G. olò, Rep. Prog. Phys. 7, (7) 69

4 r x δρ (fm - ) Sn (SLY4) - ll p n IS IV - low lying state in the interior region, proton and neutron densities are not out of phase; in the interior the isoscalar transition density dominates over the isovector one; in the surface region the contribution comes only from the neutrons. Strong isospin mixing. ew Mode r x δρ (fm - ) r (fm) ḠDR Strong isoscalar component at the surface region. Therefore, the mode can be excited by an isoscalar probe. the proton and neutron densities oscillate with opposite phases; isovector transition density much larger than the isoscalar one.

5 From an experimental point of view, the evidence for these states comes almost from oulomb excitation processes. As known, these can only provide values of the multipole B(Eλ) transition rates: [ F " B(E) ] r + To our opinion, if we want to understand their nature we should explore these states with reactions where the nuclear part of the interaction is involved. This can be done because of the strong isoscalar component of the state. By tuning the projectile mass, charge, bombarding energy and scattering angle one can alter the relative role of the nuclear and oulomb components, as well as the isoscalar and isovector contributions.

i j where H A = H A + W A ( t) t-dependence through R(t) The time dependent state is #, $ % >= ( ) ie t t A t e " > coupled

6 The two nuclei move according to a classical trajectory while quantum mechanics is used to describe the internal degrees of freedom H = H A + H B W A (t) = < i U B ( R (t)) j > a + i a j + h.c. i j where H A = H A + W A ( t) t-dependence through R(t) The time dependent state is #, $ % >= ( ) ie t t A t e " > coupled channel equations A α (t) = i α e i(e α E α )t < Φ α W (t) Φ α >A α (t) % % % Probability to excite the state P (b) = A (t =") b impact parameter its cross section is T(b): transmission coefficient

## U ( r ) = " A ( r ) v (r )" a ( r ) d r d U ( r ) = $$ [" An ( r ) #" Ap ( r ) ] % %v (r )[" an ( r ) #" ap ( r )]d r d r = r + r " r In the case ρn= /Z ρ ; ρp= /A ρ U (r α )= a Z a A Z

7 The nucleon nucleon interaction depends on the isospin where τi are the isospin of the nucleons. This implies The double folding potential has two terms where v = v ( r ) + v ( r ) " v nn = v pp = v + v ; v np = v v. ## U ( r ) = " A ( r ) v (r )" a ( r ) d r d U ( r ) = $$ [" An ( r ) #" Ap ( r ) ] % %v (r )[" an ( r ) #" ap ( r )]d r d r = r + r " r In the case ρn= /Z ρ ; ρp= /A ρ U (r α )= a Z a A Z A a A ρ A (r )v (r )ρ a (r ) dr dr. r r Double Folding procedure r r r r A a Therefore the nuclear form factors are F (r ) = $$ ["# An ( r ) +"# Ap ( r ) ] % %v (r )[# an ( r ) +# ap ( r )]r dr r dr F (r ) = $$ ["# An ( r ) &"# Ap ( r ) ] % %v (r )[# an ( r ) &# ap ( r )]r dr r dr As before, in the case one of the two nuclei has =Z then F is zero.

8 3 Sn + α 3 Sn Sn + 48 F (r) (MeV) ll ll ll The oulomb contribution is very different for the two states, while the nuclear one is of the same order of magnitude. The isospin part is important only for r (fm) r (fm) r (fm) v (r) = 7999 e 4r 4r v (r) = 4886 e 4r 4r 34e.5r.5r 76e.5r.5r 6δ(r) + 7δ(r) folding done with the effective nucleon-nucleon M3Y interaction G. R. Satchler, Direct uclear Reactions, Oxford University Press 983.

9 Square of the formfactors at the surface. State E harm (MeV) EWSR(%) Different reactions alter the relative intensity of the and states. This is due also to the different interplay of isoscalar and isovector contributions. - ll () ll hl Sn + α 3 Sn Sn + 48 F (MeV )

10 3 Sn 3 MeV/A π b P(b) T(b) α b (fm) Partial wave cross section For the, the nuclear part is much more important than the oulomb one. Only a limited range of impact parameters give contribution to the nuclear part (nuclear contribution are enhanced at grazing angles); for the oulomb part the range of b is much larger.

11 3 Sn + 4 dσ/de (mb/mev) MeV/u 5 3 MeV/u 5 MeV/u The continuous red lines are obtained by a smoothing folding procedure with Lorentzian of MeV width. The balance between and changes at different incident energies, because of the relative role of nuclear and oulomb contributions.

12 3 Sn + 3 MeV/u dσ/de (mb/mev) + α Predictions for the excitation of the dipole states by different projectiles (α, 4, 48 ). For 48 and 4 the excitation cross section for the is of the same order of magnitude that the one for the.

13 dσ/de (mb/mev) α Sn + 3 MeV/u all multipole states Predictions for the excitation of the states of different multipolarity by different projectiles (α, 4, 48 ). State E (MeV) EWSR % 3 Sn + 3 MeV/u GMR dσ/de (mb/mev) 6 4 α 5 5 all multipole states / L= h L= h L=3 h L= h 5 5 / / / hl GQR

14 3 Sn + 4 MeV/u 3 MeV/u dσ/de (mb/mev) MeV/u 4 MeV/u Variation of oulomb and uclear contributions as function of the incident energy. 5 5 Variation of multipoles states excitations as function of the incident energy. dσ/de (mb/mev) uclear GQR Sn + oulomb + ll GQR 3 - ll + GQR Total GQR 5 5

15 Summary We studied the nature of the low-lying dipole strength in neutron-rich nuclei, often associated to the Pygmy Dipole Resonance. The states are described within the Hartree-Fock plus RPA formalism, using the Skyrme interactions. We show how the information from combined reactions processes involving the oulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states.

Nuclear and Coulomb excitations of low-lying dipole states in exotic and stable nuclei

Journal of Physics: Conference Series Nuclear and Coulomb excitations of low-lying dipole states in exotic and stable nuclei To cite this article: E G Lanza et al 2013 J. Phys.: Conf. Ser. 420 012147 View