heavy ion transfer reactions studied with prisma+clara
DESCRIPTION
Heavy ion transfer reactions studied with PRISMA+CLARA. L.Corradi Laboratori Nazionali di Legnaro – INFN, Italy. Transfer reactions (multinucleon) among heavy ions. The quasi-elastic regime is governed by - form factors < f I V int I i > (structure) - PowerPoint PPT PresentationTRANSCRIPT
LEA, Catania, 13-16 October, 2008
Heavy ion transfer reactions studied Heavy ion transfer reactions studied with PRISMA+CLARA with PRISMA+CLARA
Heavy ion transfer reactions studied Heavy ion transfer reactions studied with PRISMA+CLARA with PRISMA+CLARA
L.CorradiLaboratori Nazionali di Legnaro – INFN, Italy
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Transfer reactions (multinucleon) among Transfer reactions (multinucleon) among heavy ionsheavy ions
Transfer reactions (multinucleon) among Transfer reactions (multinucleon) among heavy ionsheavy ions
The quasi-elastic regime is governed by
- form factors < f I Vint I i > (structure)
- optimum Q-values (dynamics)
degrees of freedom
single particle states
surface vibrations
pair modes
couplings
inelastic: collective ff
transfer: single particle ff
pair ff (macroscopic)
The understanding of low energy heavy ion reactions requires a careful and consistent experimental and theoretical work
- elastic scattering (nuclear potential)
- inelastic scattering (phonon form factor)
- one particle transfer (single particle form factors)
- two particle transfer (nucleon-nucleon correlations)
- multiple particle transfer (multipair transfer, ... towards DIC)
mandatory a complete set of observables
A, Z, TKEL, dσ/dΩ, σtot
THE PRISMA SPECTROMETER + CLARA GAMMA ARRAY
IC
MWPPAC
A physical event is composed by the A physical event is composed by the parameters:parameters:
•position at the entrance position at the entrance x, y x, y •position at the focal plane position at the focal plane X, YX, Y•time of flight time of flight TOF TOF•energy energy DE, EDE, E
A physical event is composed by the A physical event is composed by the parameters:parameters:
•position at the entrance position at the entrance x, y x, y •position at the focal plane position at the focal plane X, YX, Y•time of flight time of flight TOF TOF•energy energy DE, EDE, E
PRISMA spectrometer – trajectory PRISMA spectrometer – trajectory reconstruction reconstruction
PRISMA spectrometer – trajectory PRISMA spectrometer – trajectory reconstruction reconstruction
PRISMA spectrometer – trajectory PRISMA spectrometer – trajectory reconstruction reconstruction
PRISMA spectrometer – trajectory PRISMA spectrometer – trajectory reconstruction reconstruction
ΔE-E
q
A/q
Mass
Elastic scattering – using Prisma and Clara Elastic scattering – using Prisma and Clara informationinformation
Elastic scattering – using Prisma and Clara Elastic scattering – using Prisma and Clara informationinformation
elastic scattering is the first important ingredient for nuclear
reaction studies. It provides information on the (outer part
of) nuclear potential
grazing code
Differential cross Differential cross sections sections
Differential cross Differential cross sections sections
forward part : mainly reflects the behaviour of the form factors
backward part : mainly reflects the absorption
Total cross Total cross sections sections
Total cross Total cross sections sections
successive transfer
S.Szilner et al, Phys.Rev.C76(2007)024604
multinucleon multinucleon transfer :transfer :experiment vs. experiment vs. theory theory
multinucleon multinucleon transfer :transfer :experiment vs. experiment vs. theory theory
data : LNL
theory : GRAZING code and CWKB
Evaporation processes in multinucleon transfer Evaporation processes in multinucleon transfer reactionsreactions
Evaporation processes in multinucleon transfer Evaporation processes in multinucleon transfer reactionsreactions
Evaporation processes Evaporation processes directly identified with directly identified with PRISMA+CLARA An example: PRISMA+CLARA An example: 4040Ca+Ca+9696Zr at 152 MeV Zr at 152 MeV
Evaporation processes Evaporation processes directly identified with directly identified with PRISMA+CLARA An example: PRISMA+CLARA An example: 4040Ca+Ca+9696Zr at 152 MeV Zr at 152 MeV
4040Ca+Ca+9696ZrZrE=152 MeV E=152 MeV
4040Ca+Ca+9696ZrZrE=152 MeV E=152 MeV
TKEL distributions – Prisma vs. TKEL distributions – Prisma vs. Prisma+ClaraPrisma+Clara
TKEL distributions – Prisma vs. TKEL distributions – Prisma vs. Prisma+ClaraPrisma+Clara
TKEL TKEL distributions distributions
TKEL TKEL distributions distributions
pure proton stripping
Pair Pair transfer transfer
Pair Pair transfer transfer
Search for pairing vibrations
Measurements at sub-barrier energies
How the residual interaction acts in transfer How the residual interaction acts in transfer processes processes
How the residual interaction acts in transfer How the residual interaction acts in transfer processes processes
S.Szilner et al, Eur.Phys.J. A21, 87(2004)
strength function (shell model calculations)
Strong population close to the pairing vibrational region in Strong population close to the pairing vibrational region in 4040Ca+Ca+208208PbPb
Strong population close to the pairing vibrational region in Strong population close to the pairing vibrational region in 4040Ca+Ca+208208PbPb
S.Szilner et al, Phys.Rev.C76(2007)024604
Multineutron and multiproton transfer channels near closed-Multineutron and multiproton transfer channels near closed-shell nucleishell nuclei
Multineutron and multiproton transfer channels near closed-Multineutron and multiproton transfer channels near closed-shell nucleishell nuclei
PRISMA spectrometer data
GRAZING code calculations
Mass [amu]
pure neutron pick-up channels
9090Zr+Zr+208208Pb EPb Elablab=560 =560 MeVMeV
9090Zr+Zr+208208Pb EPb Elablab=560 =560 MeVMeV
L.Corradi et al, Nucl.Phys.A787(2007)160
2240
1874
3308
3842
Population of states close to the Population of states close to the pairingpairing vibrational region vibrational region
Population of states close to the Population of states close to the pairingpairing vibrational region vibrational region
Sub-barrier transfer Sub-barrier transfer reactionsreactions
Sub-barrier transfer Sub-barrier transfer reactionsreactions
- few reaction channels are opened, i.e. W(r) very small
- one has a much better control on the form factors
F(r)inel has a decay length ~ 0.65 fm F(r)tr has a decay length ~ 1.3 fm nuclear couplings are dominated by transfer processes
- Q-value distributions get much narrower than at higher energies
- one can probe nucleon correlation close to the g.s.
At energies lower than the Coulomb At energies lower than the Coulomb barrier : barrier :
At energies lower than the Coulomb At energies lower than the Coulomb barrier : barrier :
data are very scarse or almost non existing
absorptive potential form factor
Q-value window
Detection of (light) target like ions in inverse kinematics with Detection of (light) target like ions in inverse kinematics with PRISMAPRISMA
Detection of (light) target like ions in inverse kinematics with Detection of (light) target like ions in inverse kinematics with PRISMAPRISMA
PRISMA
measurements have been performed for multinucleon transfer channels and at energies well below the barrier
beam direction
20o
94Zr 40Ca
SSBD (rutherford sc.)
GRAZING code calculations for GRAZING code calculations for 4040Ca+Ca+9494Zr Zr transferstransfers
GRAZING code calculations for GRAZING code calculations for 4040Ca+Ca+9494Zr Zr transferstransfers
differential cross sections
total cross sections
A.Winther, program GRAZING http://www.to.infn.it/~nanni/GRAZING
Prisma acceptance
9494Zr+Zr+4040Ca, ECa, Elablab=330 MeV, =330 MeV, θθlablab=20=20oo, inverse , inverse kinematics kinematics
9494Zr+Zr+4040Ca, ECa, Elablab=330 MeV, =330 MeV, θθlablab=20=20oo, inverse , inverse kinematics kinematics
Mass distributions for pure neutron pick-up Mass distributions for pure neutron pick-up channels channels
Mass distributions for pure neutron pick-up Mass distributions for pure neutron pick-up channels channels
TKEL distributions for pure neutron pick-up TKEL distributions for pure neutron pick-up channels channels
TKEL distributions for pure neutron pick-up TKEL distributions for pure neutron pick-up channels channels
Qgs
Mass vs Q-value matrix for (-1p) channels channels (EMass vs Q-value matrix for (-1p) channels channels (Ell=315 =315 MeV)MeV)
Mass vs Q-value matrix for (-1p) channels channels (EMass vs Q-value matrix for (-1p) channels channels (Ell=315 =315 MeV)MeV)
background free spectra with transfer products at very low excitation energy :
no evaporation effects and cleanest conditions for comparison with theory
Experimental vs Theoretical cross sections for +1n and -1p Experimental vs Theoretical cross sections for +1n and -1p channelschannels
Experimental vs Theoretical cross sections for +1n and -1p Experimental vs Theoretical cross sections for +1n and -1p channelschannels
very
pre
limin
ary
with neutron rich with neutron rich beams...beams...
with neutron rich with neutron rich beams...beams...
C.H.Dasso, G.Pollarolo and A.Winther, Phys.Rev.Lett.73, 1907 (1994)
neutron pick-up and proton stripping
equal directions
neutron stripping and proton pick-up
Change of population pattern in going from Change of population pattern in going from neutronneutron poor to neutron rich nuclei (theoretical)poor to neutron rich nuclei (theoretical)
Change of population pattern in going from Change of population pattern in going from neutronneutron poor to neutron rich nuclei (theoretical)poor to neutron rich nuclei (theoretical)
with (moderately n-rich) heavy ions one can populate (nn), (pp) and (np) channels with comparable strength
Multinucleon transfer Multinucleon transfer reactions reactions
Multinucleon transfer Multinucleon transfer reactions reactions
GRAZING code
One needs to learn whether and to what extent the degrees of freedom and the corresponding matrix elements tested with stable beams can
hold with radioactive beams. In particular whether the form factors for one and two particle transfer and their strength need to be modified
neutron-proton correlations (np channel)
Multinucleon transfer reactions with radioactive Multinucleon transfer reactions with radioactive beams beams
Multinucleon transfer reactions with radioactive Multinucleon transfer reactions with radioactive beams beams
140Snonset of supercurrents (neutron rich nuclei)
SummarSummary y
SummarSummary y
- Multinucleon transfer processes provide important information on the interplay between reaction mechanism and nuclear structure. The Prisma spectrometer coupled to large gamma arrays is a powerful tool to study the fine details of such processes.
- The degrees of freedom involved in multiple particle transfers can be quantitatively probed only when a complete set of observables (A,Z,TKEL, dσ/dΩ, σtot) is available. This is important also for the correct description of the transition from quasi-elastic to deep-inelastic regime and other competing reaction processes (e.g. sub-barrier fusion).
- Pair modes are presently being investigated looking at the decay of (possible) pair vibrational states and via extreme sub-barrier transfer of nucleons.
A.M.Stefanini, E.Fioretto, A.Gadea, B.Guiot, N.Marginean, P.Mason, R.Silvestri, G.de Angelis, D.R.Napoli, J.J.Valiente-
Dobon
Laboratori Nazionali di Legnaro – INFN, Italy
S.Beghini, G.Montagnoli, F.Scarlassara, E.Farnea, C.A.Ur, S.Lunardi, S.Lenzi, D.Mengoni, F.Recchia, F.della Vedova
Universita’ di Padova and INFN, Sezione di Padova
S.Szilner, N.Soic, D.Jelavec
Ruđer Bošković Institute, Zagreb, Croatia
G.Pollarolo
Universita’ di Torino and INFN, Sezione di Torino, Italy
F.Haas, S.Courtin, D.Lebhertz, M.-D.Salsac
IReS, Strasbourg, France
+ CLARA collaboration
R.C. Ragaini et al., PRC2(1970)1020
L=0 transitions92Zr(p,t)90Zr
86Sr(t,p)88Sr
Pairing vibrations : light ion Pairing vibrations : light ion reactions reactions
Pairing vibrations : light ion Pairing vibrations : light ion reactions reactions
Pairing vibration Pairing vibration model model
Pairing vibration Pairing vibration model model
R.Betts et al., PRL59(1987)978
58Ni + xSn
detection of (heavy) target like ions with recoil mass detection of (heavy) target like ions with recoil mass spectrometersspectrometers
detection of (heavy) target like ions with recoil mass detection of (heavy) target like ions with recoil mass spectrometersspectrometers
RMS
measurements have been performed at subbarrier energies but for only one nucleon transfer and with very poor Q-value resolution
Absolute cross sections for one and two-nucleon transfer Absolute cross sections for one and two-nucleon transfer reactionsreactions
Absolute cross sections for one and two-nucleon transfer Absolute cross sections for one and two-nucleon transfer reactionsreactions
B.F.Bayman and J.Chen, PRC26(1509)1982
E ~ Eb
direct
successive
successive
direct
E << Eb
one+two step calculations undepredict the data by a factor ~ 2
one+two step calculations undepredict the data by 25-30%
208Pb(16O,18Og.s.)206Pb
G.Pollarolo, Phys.Rev.Lett.100,252701(2008)
Quasielastic barrier distributions : role of particle transfer Quasielastic barrier distributions : role of particle transfer channelschannels
Quasielastic barrier distributions : role of particle transfer Quasielastic barrier distributions : role of particle transfer channelschannels
sub-barrier transfer cross section measurements are important to compare with fusion cross sections in a similar energy and angular momentum range
A.M.Stefanini et al., PRC76,014610(2007)
Sub-barrier fusion of Sub-barrier fusion of 4040Ca+Ca+9494Zr Zr Interplay of phonon and transfer Interplay of phonon and transfer couplingscouplings
Sub-barrier fusion of Sub-barrier fusion of 4040Ca+Ca+9494Zr Zr Interplay of phonon and transfer Interplay of phonon and transfer couplingscouplings
2+ [2067]
2+ [2820]
2+ [1848]
2+ [3058]
0+ [4283] strong in (t,p)
2+ [3500]
0+ [2903] weak in (t,p)
0+ [3992] strong in (t,p)
0+ [3589] strong in (t,p)
2+ [934]
0+ [g.s.]
1132
1225 1463
990
934
1848
492
972
934
1742
912
439
837
1970
L=2 (t,p)
L=2 (t,p)
L=2 (t,p)
L=2 (t,p)
L=2 (t,p)
L=2 (t,p)
new
identified and known
identified but in overlap with other known
existing ?
non tabnon tab
(n,n’)
(n,n’)
208Pb(90Zr,92Zr)206Pb E=560 MeV
(4000)
(50)
(1000)
(4000)
(245)
(120)
(1100) wide peak at 893
PRISMA spectrometer – trajectory PRISMA spectrometer – trajectory reconstruction reconstruction
PRISMA spectrometer – trajectory PRISMA spectrometer – trajectory reconstruction reconstruction
X (channels)
A/q
(ch
anne
ls)
K.Sapotta et al., PRC31(1985)1297
linear diffusion : strong correlation between proton and neutron transfer
uncorrelated N and Z diffusion
Interpretation of massive transfer via diffusion Interpretation of massive transfer via diffusion modelsmodels
Interpretation of massive transfer via diffusion Interpretation of massive transfer via diffusion modelsmodels
the region with small energy loss is where nuclear structure
properties play a major role
Multinucleon transfer reactions : quasi-elastic Multinucleon transfer reactions : quasi-elastic regimeregime
Multinucleon transfer reactions : quasi-elastic Multinucleon transfer reactions : quasi-elastic regimeregime
pure neutron pick-up
pure proton stripping
N/Z equilibrization
Mass distributions for proton stripping channels channels Mass distributions for proton stripping channels channels (E(Ell=315 MeV)=315 MeV)
Mass distributions for proton stripping channels channels Mass distributions for proton stripping channels channels (E(Ell=315 MeV)=315 MeV)
Ar isotopes (-Ar isotopes (-2p) 2p)
Ar isotopes (-Ar isotopes (-2p) 2p)
K isotopes (-K isotopes (-1p)1p)
K isotopes (-K isotopes (-1p)1p)
background free spectra with transfer products at very low excitation energy :
no evaporation effects and cleanest conditions for comparison with theory
fusion
Correlation between reaction Correlation between reaction channelschannels
Correlation between reaction Correlation between reaction channelschannels
In the presence of couplings the energy of relative motion is not well defined. An exchange of energy from the relative motion to the intrinsic degrees of freedom takes place
quasi elastic, deep inelastic
quasi fission, [...]
Evaporation processes directly identified with Evaporation processes directly identified with PRISMA+CLARA PRISMA+CLARA an example : an example : 4040Ca+Ca+9696Zr reaction at 152 MeV Zr reaction at 152 MeV
Evaporation processes directly identified with Evaporation processes directly identified with PRISMA+CLARA PRISMA+CLARA an example : an example : 4040Ca+Ca+9696Zr reaction at 152 MeV Zr reaction at 152 MeV
heavy partner
light partner
-2p+2n
channel
PRISMA spectrometer – trajectory PRISMA spectrometer – trajectory reconstruction reconstruction
PRISMA spectrometer – trajectory PRISMA spectrometer – trajectory reconstruction reconstruction
E
ΔE
64Ni+238U
Elastic Elastic scatteringscattering
Elastic Elastic scatteringscattering
Inelastic Inelastic scatteringscattering
Inelastic Inelastic scatteringscattering
G.Pollarolo and A.Winther, PRC62(2000)054611
GRAZING code calculations
G.Montagnoli et al., EPJA15(2002)351
Transfer and fusion cross sections for Transfer and fusion cross sections for 4040Ca+Ca+90,9690,96ZrZr
Transfer and fusion cross sections for Transfer and fusion cross sections for 4040Ca+Ca+90,9690,96ZrZr
H.Esbensen et al, PRC57(1998)2401
exp. neutron transfer yield coupling scheme
sub-barrier fusionnear and sub-barrier transfer
Evap.Res.
Fusion
Fusion+Deep Inel.
TransferTr+Inel
2+,3-+Multiphonon
1-dim.
5858Ni+Ni+124124SSnn
5858Ni+Ni+124124SSnn
C.L.Liang et al, PRC57(1998)2393
4040Ca+Ca+9696Zr reaction : states of Zr reaction : states of particle/hole vibration character particle/hole vibration character
4040Ca+Ca+9696Zr reaction : states of Zr reaction : states of particle/hole vibration character particle/hole vibration character
nuclear binding energies deuteron transfer (light ions)
np np correlations correlations
np np correlations correlations
R.B.Cakirli et al, PRL94,092501(2005) P.Van Isacker et al, PRL94,162502(2005)
with (moderately n-rich) heavy ions one can populate (nn), (pp) and (np) channels with comparable strength
Multinucleon transfer Multinucleon transfer reactions reactions
Multinucleon transfer Multinucleon transfer reactions reactions
GRAZING code
Multinucleon transfer reactions with neutron-rich Multinucleon transfer reactions with neutron-rich beams beams
Multinucleon transfer reactions with neutron-rich Multinucleon transfer reactions with neutron-rich beams beams
possibility to populate nuclei via pick-up and stripping of both
neutrons and protons
probing (nn), (pp) and (np) correlations. Important for studies
on pairing vibrations/rotations, nuclear superfluidity
C.H.Dasso, G.Pollarolo, A.Winther, PRL73(1994)1907
GRAZING code calculations
production of neutron rich isotopes
QE/DICQE/DICQE/DICQE/DIC
U.Schroder et al., PRC16(1977)623A.D.Hoover et al., PRC25(1982)256
L.Corradi et al, PRC63(2001)021601Rg.s. Q-values
histograms: exp.
lines: CWKB theory
Strong population close to the g.s.Q-values up to +4n channels in Strong population close to the g.s.Q-values up to +4n channels in 6262Ni+Ni+206206Pb Pb
Strong population close to the g.s.Q-values up to +4n channels in Strong population close to the g.s.Q-values up to +4n channels in 6262Ni+Ni+206206Pb Pb
Search for a possible odd-even staggering effect (pair Search for a possible odd-even staggering effect (pair modes)modes)
Search for a possible odd-even staggering effect (pair Search for a possible odd-even staggering effect (pair modes)modes)
J.Giovinazzo et al., PRL99(2007)102501
Importance of nucleon-nucleon Importance of nucleon-nucleon correlationcorrelation
Importance of nucleon-nucleon Importance of nucleon-nucleon correlationcorrelation
M.V.Ricciardi et al., NPA733(2004)299
2proton decay
Ti(238U,X) 1GeV/A
the understanding of (2p) decay and U fragmentation data requires knowledge of pair effects, similarly to low energy transfer : development of nuclear structure and reaction models is essential
The transfer components and what the Grazing code can The transfer components and what the Grazing code can computecompute
The transfer components and what the Grazing code can The transfer components and what the Grazing code can computecompute
E. Fioretto - LNL66
AGATA Dem - PRISMA Workshop - LNL, 15-16 Nov 2007
70Zn+238U450 MeV
96Zr+124Sn 575 MeV
136Xe+208Pb950 MeV
40Ar+208Pb450 MeV
Z=18
Z=30
Z=40Z=54
E/E < 2% Z/Z ~ 60 for Z=20
Energy [arb. units]
A.O.Macchiavelli et al.,Phys.Lett.B480(2000)1
May T=0 collective effects show up as a vibrational phonon ?
pairing strenght
weak collective correlations
strong collective correlations, possibility to develop a permanent deformation in gauge space
Experimental excitation spectrum for addition phonons around 56Ni
Particles identified from PRISMA in Particles identified from PRISMA in the the 4848Ca+Ca+6464Ni reaction, E=320 MeVNi reaction, E=320 MeV θθlablab=30=30oo
Particles identified from PRISMA in Particles identified from PRISMA in the the 4848Ca+Ca+6464Ni reaction, E=320 MeVNi reaction, E=320 MeV θθlablab=30=30ooDIC
QE
G.Pollarolo and A.Winther, PRC62(2000)054611
GRAZING code calculations
G.Montagnoli et al., EPJA15(2002)351
Transfer and fusion cross sections for Transfer and fusion cross sections for 4040Ca+Ca+90,9690,96ZrZr
Transfer and fusion cross sections for Transfer and fusion cross sections for 4040Ca+Ca+90,9690,96ZrZr
Differential cross Differential cross sections sections
Differential cross Differential cross sections sections
Total kinetic energy loss distributions in Total kinetic energy loss distributions in 4040Ca+Ca+208208Pb EPb Elablab=235 =235 MeV MeV θθlablab=84=84oo
Total kinetic energy loss distributions in Total kinetic energy loss distributions in 4040Ca+Ca+208208Pb EPb Elablab=235 =235 MeV MeV θθlablab=84=84oo
TKEL corresponding to the two-touching sphere configuration (maximal amount of energy that can be lost in binary collisions)
40S
β decay
NSCL-MSU
(1)
GANIL
(2)PRISMA/CLARA
40S
N.Marginean, Trento Workshop, 2006
X.Liang, PRC74(2006)014311
Collectivity above N=20 shell Collectivity above N=20 shell closureclosure
Collectivity above N=20 shell Collectivity above N=20 shell closureclosure
D. Sohler et al.
PRC 66(2002)054302
J.A.Wigner et al.,
PRC 64(2001)064318
36S (230MeV) + 208Pb
40Ar(205MeV) + 170Er
S
82Ge
80Zn
reliable production cross sections for exotic nuclei like the N=50 82Ge or 80Zn are mandatory when one project γ-spectroscopy experiments
Cross sections measurements Cross sections measurements 8282Se+Se+238238U U EElablab=500 MeV=500 MeV
Cross sections measurements Cross sections measurements 8282Se+Se+238238U U EElablab=500 MeV=500 MeV
74Ni
C.H.Dasso, G.Pollarolo and A.Winther, Phys.Rev.Lett.73, 1907 (1994)
neutron pick-up and proton stripping
equal directions
neutron stripping and proton pick-up
Change of population pattern in going from Change of population pattern in going from neutronneutron poor to neutron rich nuclei (theoretical)poor to neutron rich nuclei (theoretical)
Change of population pattern in going from Change of population pattern in going from neutronneutron poor to neutron rich nuclei (theoretical)poor to neutron rich nuclei (theoretical)
GRAZING code
possibility to explore multiple particle transfers in the pick-up and stripping of both neutrons and protons
Z,A yields - time-of-flight spectrometer data (LNL)
Total cross sections – data compared with Complex WKB calculations
S.Szilner et al, Phys.Rev.C71(2005)044610
N/Z of the compound
pure proton stripping pure neutron pick-up
S.Szilner et al, Phys.Rev.C71(2005)044610
successive transfer
+ simultaneous transfer
CWKB CALCULATIONS
Pure neutron and proton Pure neutron and proton transfers transfers
Pure neutron and proton Pure neutron and proton transfers transfers
neutronsprotons
successive transfer+ simultaneous transfer
+ evaporation effects
L.Corradi et al, PRC66(2002)024606
CWKB
CALCULATIONS
Pure neutron and proton transfers in Pure neutron and proton transfers in 5858Ni+Ni+208208Pb Pb EElablab=328.4 MeV=328.4 MeV
Pure neutron and proton transfers in Pure neutron and proton transfers in 5858Ni+Ni+208208Pb Pb EElablab=328.4 MeV=328.4 MeV
J.Ball et al., PRC4(1971)196
90Zr(p,t)88Zr
The enhancement factor ε has been used to compare the experimental intensities with those calculated on the basis of specific assumptions about the nuclear wave function involved. Disagreement between theory and experiment is indicated by deviations of ε from unity.
transition amplitude
isospin coefficient normalization factor (zero range approx.)
spectroscopic amplitude
enhancement factor
D.G.Fleming et al, PR165(1968)1153
for 1p and 2s1d shells
upper bound that can be expected in comparing (p,t) and (p,3He) reactions in the limit of pure S=0 transfer for (p,3He)
due to the additional S=1 spin transfer in (p,3He), the cross section ratio should be modified
scheme of levels from the harmonic pairing model
selection rules for (one step) two nucleon transfer reactions
In (3He,p) reactions p-n pairs may be transferred either with S=0,T=1 or with S=1,T=0. In (α,d) reactions only S=1,T=0 is possible.
GANIL in-beam gamma spectroscopy (fragmentation of 48Ca)