Isospin symmetry breaking in mirror nuclei Experimental and theoretical methods Silvia M. Lenzi Dipartimento di Fisica dell Università and INFN, Padova, Italy
2. Experimental techniques for mirror spectroscopy
Coulomb Energy Differences (CED) Z Isospin symmetry manifests better along the N=Z line Analogue states with low spin are studied in CDE (IMME) What about the difference in excitation energy with increasing spin? CED have been restricted for many years to low-spin states due to the difficulties in populating p proton rich nuclei Experimental issues proton-rich rich T z < isobars only weakly populated mirrored gamma-ray energies almost identical we need very clean reaction channel selection
Populating proton-rich nuclei Fusion-evaporation 8 6 p p 4 mainly yrast states target nucleus 48 Mn 48Mn Gate: 26/636/647 reactions populate 2 199 (6 + -> 5 + ) 26 26 (6 + -> 5 + ) 3 (9 + -> 8 + ) 423 8 + ) 395 (9 + -> 8 43 (5 + -> 4 + ) 428 (5 + -> 4 + ) -> 4 + ) 636 (6 + 627 (6 + -> 4 + ) 628 (7 + -> 6 + ) 647 (7 + -> 6 + ) the Energy f(kev) 7/2 shell 948 (8 + -> 7 + ) beam 48 nucleus V 4 48V Gate: 199/627/628 3 proton 2 28 number 1 27 52 Co 2 4 6 8 1 977 (8 + -> 7 + ) 5 Fe 51 Fe 54 Ni 55 Ni 56 Ni 53 Co 54 Co 55 Co 52 Fe 53 Fe 54 Fe fusion N=Z 1-22 s 1-19 s particle evaporation compound formation n p n α 25 48 Mn 49 Mn 5 Mn 51 Mn 52 Mn 53 Mn 24 23 22 42 Ti 44 V 43 Ti 46 Cr 45 V 44 Ti 47 Cr 46 V 45 Ti 48 Cr 47 V 46 Ti 49 Cr 48 V 47 Ti 5 Cr 49 V 51 Cr 1-15 s emission γ 21 2 41 Sc 42 Sc 43 Sc 44 Sc 45 Sc 4 Ca 41 Ca 42 Ca 43 Ca 44 Ca neutron number 1-9 s ground state 2 21 22 23 24 25 26 27 28
Example: the f 7/2 shell The 1f 7/2 shell is isolated in energy from the rest of fp orbitals Wave functions are dominated by (1f n 7/2 ) configurations N=Z High-spin states experimentally reachable 28 27 proton number 52 Co 54 Ni 53 Co 55 Ni 54 Co 56 Ni 55 Co f 5/2 p 1/2 p 3/2 f 7/2 28 d 3/2 s 1/2 d 5/2 2 26 25 24 23 22 21 2 42 Ti 41 Sc 4 Ca 44 V 43 Ti 42 Sc 41 Ca 5 Fe 51 Fe 52 Fe 53 Fe 54 Fe 48 Mn 4 9 Mn 5 Mn 5 1 Mn 52 Mn 5 3 Mn 46 Cr 47 Cr 48 Cr 49 Cr 5 Cr 51 Cr 45 V 46 V 47 V 48 V 49 V 44 Ti 45 Ti 46 Ti 43 Sc 44 Sc 45 Sc 42 Ca 43 Ca 44 Ca 47 Ti neutron number 2 21 22 23 24 25 26 27 28 Experimental issue : proton-rich rich T z =-1/2 isobars are weakly populated Mirrored gamma ray energies almost identical need very clean reaction channel selection
Experimental requirements High efficiency and resolution for γ detection Low cross section at high spin (small masses) High energy transitions Good selectivity: it particle detectors t Many channels opened: high efficient charged-particle detectors Kinematics reconstruction for Doppler broadening Mass spectrometers Neutron detectors to select proton-rich channels Polarimeters and granularity (J, π, δ)
Gamma spectroscopy gamma ray Anti-Compton Constructing a level scheme Ge crystal Gamma array γ 1 156 Dy γ 2 γ 3
Gamma-ray spectrometers Conventional techniques New technique: tracking GASP GAMMASPHERE AGATA GRETA 1 5% ( M =1 M =3) 4 2 % ( M =1 M =3)
Techniques for proton-rich spectroscopy Three basic techniques for selecting proton-rich systems 1. High efficiency & high granularity gamma-ray spectrometer high fold n (n 3) coincidence spectroscopy 2. Gamma-ray array + mass spectrometer + focal plane detectors - identify A,Z of recoiling nucleus and ToF tag emitted gamma-rays 3. Identify cleanly all emitted particles from reaction - needs a charged-particle detector array + high-efficiency & high granularity neutron detector array + γ-ray array
1. High-fold -coincidence spectroscopy Rely on the power of the array: high-fold gamma ray coincidences high h granularity and on the similarity between the energy of the transitions with those of the known mirror nucleus Double-coincidence spectra after gating on 2 analogue transitions 32 32 S S 24 24 53 Mg,1p2n Co 53 Mg,2p1n Fe 26 ms S.J. Williams et al., Phys. Rev. C 68 (23) 1131
2. Identify A and Z of the recoiling nucleus Fragment Mass Analyser GS Combined electric and magnetic dipoles beam rejection & A/q separation A/q identified by x-position at focal plane Z identified ed by energy e loss (E- E) in gas-filled ionisation o chamber information used to tag coincident gamma-rays at target position Efficiency -up to ~ 15% Measure the final residue
An example: the A=48 mirror pair 48 48 25Mn23-23V 25 48 48 Mn V ~ 1 4 Need very good selectivity E Z identification Ionisation o Chamber 5 E 15 Fe 1 6 5 4 3 2 1 5 4 3 2 1 Co ounts 4 3 2 1 3 2 1 Mn Cr V Ti 2 4 6 8 1 12 14 16 18 2 Energy (kev) A/q selection at the focal plane + gate on Z=25 Cou unts 3 25 2 15 1 5 M.A. Bentley et al., Phys. Rev. Lett. 93 (26) 13251 * * * ## * #* * * * * # 51 Mn 54 Mn ** 5 1 Energy (kev) 15 2
Selecting pure spectra Contaminants can be removed by using the recorded total energy E and time-of-flight (TOF) of the recoils Mass is proportional to ET 2 E 1 mv 2 m E 2, TOF 2 d v TOF the ET 2 information has sufficient resolution to distinguish three mass units difference. Co ounts 3 25 2 15 1 5 91 26 159 43 286 423 224 38 582 636 647 948 137 48 Mn 1594 1686 5 1 15 2 Energy (kev) 1954 25 2 15 1 5 Coun 4 3 2 1 nts5 Total A = 51 15 A = 54 1 5 5 1 15 E(TOF) 2 M.A. Bentley et al., Phys. Rev. Lett. 93 (26) 13251
γ-γ coincidence analysis 8 6 4 2 2 6 (6 + -> 5 + ) 423 (9 + -> 8 + ) 43 3 (5 + -> 4 + ) 636 (6 + -> 4 + ) 64 47 (7 + -> 6 + ) Gate: 26/636/647 48 Mn (A/q = 3, Z=25)-gated and 948 (8 + -> 7 + ) E(TOF) 2 -gated - coincidence analysis 4 3 2 1 199 (6 + -> 5 + ) 395 (9 + -> 8 + ) 428 (5 + -> 4 + ) 627 (6 + -> 4 + ) 628 (7 + -> 6 + ) 48 V Gate: 199/627/628 977 (8 + -> 7 + ) 2 4 6 8 48 1 Energy (kev) 48 Mn 48 V 25 23 23 25 M.A. Bentley et al., Phys. Rev. Lett., 97 (26) 13251
Fragmentation reactions and exotic beams Fragmentation reactions with the removal of 5 or more particles are mainly of statistical character and populate yrast states. One knock-outout reactions are a direct process. Two proton knockout from neutron-rich nuclei and two neutron knockout from proton-rich nuclei at intermediate t or relativistic i bombarding b energies are also direct reactions. Direct reactions selectively populate single-hole states Between 3 and 5 nucleons removed the two processes compete Fragmentation reactions are particularly suitable to populate mirror nuclei far from stability and near the proton dripline. 15
Knockout reactions with exotic beams Example: study the magicity of 36 Ca mirror of magic 36 S (N=2, Z=16) One neutron removal reaction from 37 Ca beam Technique pioneered at GANIL (Stanoiu et al. PRC 69, 34312 (24)) 36 Ca 327(16) kev F. Azaiez et al.
Mirrored fragmentation of N=Z nuclei MSU experiment 6 mg/cm2 Be target S8 Spectrograph 1pnA 58 Ni 188 mg/cm 2 Be Primary N=Z second. mirrored frag. Drip line 58 Ni 53 Ni Mn 56 Ni 53 Ni J.R. Brown et al., Phys. Rev. C 8, 1136(R) (29) 17
Mirror nuclei with multinucleon transfer A & Z identification PRISMA Prisma + CLARA @LNL, Italy in-beam -ray CLARA Efficiency ~ 3 % Peak/Total ~ 5 % FWHM ~ 1 kev @ v/c = 1%
Mirror nuclei with multinucleon transfer 32 S 58 Ni @ 135 MeV LNL, N. Marginean 29 P 61 Cu 29 61 Si Zn PRISMA CLARA
3. Measuring the evaporated particles With this method we do not measure directly the final residue but the particles emitted from the compound nucleus charged particles neutrons We need detectors with high efficiency Advantage: more flexible than recoil mass spectrometry more channels can be measured! Disadvantage: not as clean as RMS If neutrons are needed, it may be much less efficient
Charged-particle detectors DIAMANT 86 CsI(Tl) elements scintillators efficiency: protons ~7% alphas ~ 5% EUCLIDES Si E-ΔE telescopes efficiency: protons ~7% alphas ~ 4%
Time of fligh ght Neutron detection systems neutrons 1 3 Gammas 2 neutrons EXOGAM + N-Wall @ GANIL Zero cross-over Detectors placed downstream of the target position Large volume liquid scintillators coupled to photo-multipliers tubes. U Usually ll replace l some off th the fforward-most d t Ge G detectors d t t off the th array Efficiency ~ 25%
246 292 954 1461 1814 416 33 1561 6 787 884 / 888 1164 / 1543 468 1371 369 184 Discrimination using time-of-flight data Problem: one neutron scattered between two detectors looks like two neutrons A single scattered neutron different times-of-flight flight recorded Genuine 2-neutron event similar timeof-flight recorded 2 15 1 5 no stringency gates 3 25 Pure 2n spectrum 44 44 Ti (2p,2n channel) Ti 45 V 45 V (p,2n channel) 6 5 4 3 2 1 highest level of stringency 19 2 21 Time-of-Flight Difference Co ounts 2 15 1 5 5 1 15 2 25 Energy (kev)
An example: production of 5 Fe Experiment for 5 Fe, LNL 28 28 56 * 14Si14 14Si14 28Ni28 5 24Cr26 2 p 5 26Fe 24 2n fus ~ 3mb fus ~. 3mb EUROBALL: High efficiency (e ph ~8%) and high granularity (29 crystals) HpGe array. 26 Clover detectors ( 4 crystals) & 15 Clusters ( 7 crystals). ISIS: Charged-particle detector array - 4 Si E-DE telescopes, total efficiency e p ~7%, e a ~4% NEUTRON WALL: 5 detector elements - BC51A Liquid Scintillator. Efficiency (reaction dependent) e 1n ~25%. S.M. Lenzi et al., Phys. Rev. Lett 87 (21) 12251
First observation of excited states in 5 Fe 11 + 6994 1581 627 1 + 6367 12 + 761 662 11 + 6949 61 1 + 6339 1595 8 + 4786 8 + 4744 1627 1581 6 + 3159 6 + 3163 765 1 87 138 4 + 1852 4 + 1881 2 + 765 + 5 Fe 26 24 1282 1 98 2 + 783 + 5 783 Cr 24 26 counts 2 16 *+ of gates (*) *2+ 5 Fe sum 12 765 187 8 138 627 1627 4 1581-4 6 5 4 3 2 1 11 + 1 + 11 + 1 + 61 12 + 11 1 + 662 2 + 783 + *2+ 4 + 198 *2+ 4 + 4+ *6+ * 6 + 4 + 1282 1 + 8 + 8 + 6 + 5 Cr sum of gates (*) 1581 1595 6 7 8 9 1 11 12 13 14 15 16 17 E (kev) 6 + 8 + 1 + 8 + σ(fe)/ σ(cr) 1-4 SML et al., Phys. Rev. Lett. 87, 12251 (21)
Spectroscopy with exotic stopped beams Fragmentation of 58 Ni beam 54 Secondary beam of 54 Ni in the isomeric state 1 + + 8 + 1 + 6 + 4 + 54 Ni 2 + 4 + 2 2 + + 8 + 6 + 6 + 1 + States in 54 Ni known up to the 6 +, A.Gadea et al. Phys. Rev. Lett. 97 (26) 15251 (EB+EUCLIDES+N-Wall) D. Rudolph et al., Phys. Rev. C 78, 2131(R) (28)
Gamma and proton decay of 54 Ni Full analysis lifetime D. Rudolph et al., Phys. Rev. C 78, 2131(R) (28) branching ratio MED proton decay
3. Theoretical tools for CED First part
Basic Shell Model The hamiltonian (only two-body forces) spherical mean field U(r) is a central (1-body) potential 4 Centrifugal 2 Coulomb 2 (fm)) 4 R (f -2-4 Configuration Nuclear -6 29
Configuration mixing Mixing of configurations due to the residual interaction
Effective Hamiltonian We limit the space to a reduced set of shells. The Hamiltonian becomes an effective hamiltonian H eff that accounts for the missing space. H eff H m H M monopole Multipole H m - unperturbed energy of the different configurations in which the valence nucleons are distributed - determines the single particle energies - dominant role far from stability H M - correlations - mixing of configurations - coherence - energy gains 31
Effect of the correlations The multipole Hamiltonian HM i d is dominated i t db by th the pairing i i and d the quadrupole-quadrupole forces The fact that some nuclei display collective behaviour depends on the structure of the spherical field near the Fermi surface for both protons and neutrons 32
Ingredients for the Shell Model calculations 1) an inert core 2) a valence space 3) an effective interaction that mocks up the general hamiltonian in the restricted basis the valence space The choice is determined by the limits in computing time and memory: large inert core dimension of the matrices to be diagonalised. Current codes diagonalize matrices of dimension ~1 1 28 2 8 2 N or Z f 5/2 p 1/2 p 3/2 f 7/2 d 3/2 s 1/2 d 5/2 p 1/2 p 3/2 s 1/2
Shell model and collective phenomena Shell model calculations in the full fp shell h ll give i an excellent ll t d description i ti of the structure of collective rotations in nuclei of the f7/2 shell
Mirror energy differences and alignment j J j probability distribution for the relative distance of two like particles in the f7/2 shell j j E C 8 8 j j 6 neutron align. 4 2 j j A(N,Z) A(Z,N) 6 J=6 proton 4 align. 2 j j J= J.A. Cameron et al., Phys. Lett. B 235, 239 (199) MED I=8 angular momentum Shifts between the excitation energies of the mirror pair at the back-bend indicate the type of nucleons that are aligning Silvia Lenzi Ecole Internationale Joliot-Curie, September 21
Nucleon alignment at the backbending J.A. Cameron et al., Phys. Lett. B 235, 239 (199) C.D. O'Leary et al., Phys. Rev. Lett. 79, 4349 (1997) j j Experimental MED j j J=6 Alignment MED are a probe of nuclear structure: reflect the way the nucleus generates its angular momentum Silvia Lenzi Ecole Internationale Joliot-Curie, September 21
Nucleon alignment at the backbending D.D. Warner, M.A. Bentley and P. Van Isacker., Nature Physics 2 (26) 311 Energy (MeV) 6 51 F e 51 Mn t Experiment fp-shell Mo od Experiment Shell Model 25 MED Alignment 21 3 17 2J 13 9 1-1 5 MED (kev) Silvia Lenzi Ecole Internationale Joliot-Curie, September 21
Alignment and shell model Define the operator J 6 J 6 A a a a a Counts the number of protons coupled to J=6 ΔA Calculate the difference of the expectation value in both mirror as a function of the angular momentum Z J ' J A Z J, J J A ' 7/2 5/2 3/2 1/2 51 Fe 51 Mn In 51 Fe ( 51 Mn) a pair of protons (neutrons) align first and at higher h frequency align the neutrons (protons) Alignment 51 Fe- 51 Mn M.A.Bentley et al. Phys Rev. C62 (2) 5133 Silvia Lenzi Ecole Internationale Joliot-Curie, September 21
Alignment in odd- and even-mass nuclei In odd-mass nuclei, the type of nucleons that aligns first is determined d by the blocking effect the even fluid will align first 7/2 5/2 3/2 1/2 51 Fe 51 Mn What about even-even rotating nuclei? 5 Fe 5 Cr Silvia Lenzi Ecole Internationale Joliot-Curie, September 21
Alignment in even-even rotating nuclei Shell Renormalization model only qualitative of the Coulomb description m.e.? Only a Coulomb effect? calculate for protons in both mirrors: ΔA J A Z J ' J A Z ' J Cr-Fe counts the number of aligned protons - ΔA can shell model do better? Silvia Lenzi Ecole Internationale Joliot-Curie, September 21 In 5 Cr ( 5 Fe) a pair of protons (neutrons) align first and at higher frequency align the neutrons (protons) S.M.Lenzi et al., Phys. Rev. Lett. 87, 12251 (21)
Lecture 2 The end