2. MoNMoN MoNA Talk July 20 Kirby Kemper Florida State University

3. Nuclear reactions change a given set of nuclei into other nuclei. With them we can achieve the long sought transformation of elements As far as we know the first observation of a nuclear reaction was when Rutherford’s students observed very long range “alpha”particles coming from the radioactive sources that they were using for their elastic scattering measurements. The reaction they were observing was 14 N(α,p) 17 O

4. Nuclear Reactions- Many Names: Compound Nucleus Direct Fusion Fission Deep Inelastic Scattering Resonances

5. Simplest process and most probable of happening is elastic scattering. Here projectile scatters from target and comes in in its ground state and is detected in its ground state. You can also have inelastic scattering where no mass is transferred between the target and projectile but only energy.

6. Some notation notes: Normal Kinematics: target( beam, outgoing) residual nucleus 14N(α,p)17O “beam” particles are lighter than the target nuclei Inverse kinematics: 4 He( 14 N, 17 O)p heavy beam strikes lighter target For a lot of radioactive beam work we are working in inverse kinematics where we might have a 48 Ca beam striking a 9 Be target and knock six protons and four neutrons from the beam to make 38 Si and then the 38 Si strikes another 9 Be target where two protons are knocked out to make 36 Mg, the nucleus of interest 9 Be( 48 Ca, 38 Si) 23 Ne 9 Be( 38 Si, 36 Mg) 11 C Start with 50pnA of 48 Ca make 4000 38 Si per second or 3x10 11 48Ca particle/sec to make 4000 38Si/sec to then make 15 36 Mg per hour

8. Direct Reaction- Takes place quickly~ 10 -22 sec time it takes for a nucleon to cover the width of a nucleus single step that links the initial nuclear state with the final one Compound Reaction- multi-step process where the compound nucleus forgets how it was formed formation and decay are independent overlap of initial and final states does not enter into analysis

9. There are two ways in which physics tries to obtain a consistent picture of the structure of the atomic nucleus. One of these is the study of the elementary particles, their properties and mutual interactions. Thus one hopes to obtain a fundamental knowledge of the nuclear forces, from which one can then deductively understand the complicated nuclear structures. The other way consists in gaining, by direct experimentation, as many different data as possible for individual nuclei, and examining the relations among these data. One expects to obtain a network of correlations and connections which indicate some elementary laws of nuclear structure. These two ways have not yet met to establish a complete understanding of the nucleus, although many connections have been found. From Introduction to “Elementary Theory of Nuclear Shell Structure” M.G. Mayer and J.H.D. Jensen 1955 p vii

10. So, our job is to learn about nuclear structure and or reaction models with any tool at our disposal Reactions where we detect the charged particles gammas and neutrons produced Beta decay with neutrons, charged particles and gammas Magnetic moments

11. What has made it possible to study nuclei like 36Mg are greatly more efficient detection systems MoNA is one such system where a system had to be built that would handle the much higher neutron energies that occurred with the use of the coupled cyclotrons that would let us make nuclei much closer to the neutron dripline The new complicated systems require collaborations of many individuals to make them work Lets pick on example of study: structure of nuclei at the neutron dripline

13. Just as need new ion source and detector systems for the study of these exotic nuclei we need new theoretical techniques to handle the calculation of nuclear structure and reactions of nuclei that are either just bound or in fact are unbound Consider elastic scattering- a well understood process for heavy-ions

14. Huge change in computing capability allows for both new experimental systems by integrating the computer into the detection system and new theory capabilities. In 1976 on calculation took 50,000 cpu seconds and cost $1000 Today same calculation takes 3 seconds on my laptop and costs???.00001 cents Not speed of computer but cheap memory However, we are now learning what physics we don’t understand becausewe can put in physics effects that weren’t possible before

15. Classic Fresnel scattering problem

17. Take a few examples of how we develop nuclear structure Knowledge Coulomb Excitation (tells us about the proton properties) Extract B(C2) to learn about the mass properties do inelastic proton scattering extract B(E2) Mass (particle) transfer reactions

18. In-beam spectroscopy with fast beams at rates of a few nuclei per second N R  × N T × N B  Cross section –N T Atoms in target –N B Beam rate –N R Reaction rate Example  = 100 mbarn –N T = 10 21 cm -2 –N B = 3 Hz –N R =26/day = 3×10 -4 Hz Fast exotic beams allow for – thick secondary targets (100- 1000 thicker than at low energy) – event-by-event identification – Clean trigger beamtarget scattered beam Luminosity gain of 100-1000 … … measure recoils and use photons to indicate inelastic scattering

19. Intermediate-energy Coulomb excitation Reduced transition matrix elements independent of impact parameter Experiment: Max.  determines min. b A. Gade et al., Phys. Rev. C 68 (2003) 014302. adopted

20. Our definition of a direct reaction selective population of the same states in the final nucleus at several bombarding energies that are different by no more than a factor of 2 or so by the same reaction ((d,p) at 7.5 MeV/amu and 15 MeV/amu) selective population of the same states in the final nucleus by different reactions that transfer the same particle (say one proton or one neutron) (d,p) ( 7 Li, 6 Li) ( 13 C, 12 C)

21. Here we have selective population but states populated change rapidly as beam energy changes. Not Direct Reaction

23. Why do we repeat reactions that seem to give the same information? For example, (d,n) ( 3 He,d) (α,t) ( 7 Li, 6 He) ( 16 O, 15 N) we can populate levels with different intensities by using angular momentum mismatch, and the fact that the transferred proton comes from different orbits in the projectile (α,t) will favor high spin orbits compared with (d,n) use every trick we know to get info

24. So now you have measured a cross section (the probability for a transition to occur What does it tell us about the nucleus? Here we need theory For mass transfer first try what is known as the distorted wave theory or DWBA –used a low energies (10 MeV/amu) From this theory you can learn the spin of the nuclear states you are populating and also theory probability of looking like the target+particle

25. Distorted Wave Born Approximation (DWBA)

26. A simple one step stripping reaction may be written diagramatically as A + a → B + b A + (b + x) a → (A + x ) b + b where A represents the target core, b represents the projectile core, and x is the transferred mass which may represent any number of particles.

27. DWBA Formalism (d,p) Initial State Interaction Final State

28. Assumptions of DWBA Single Step transfer of nucleon to target-core. –1 st Born Approx., 1-step process, Direct –Core is not excited in process –Projectile remains in ground state Distorted Waves derived from elastic scattering –Assumes wave does not change much during scattering Transfer reactions are weak compared to elastic scattering. This formulation is spin-independent.

29. Spectroscopic Factor Parentage: Sum over all possible configurations of target and nucleon states that produce final state. Only one of these (A’=A) is the pure single-particle state in DWBA. Amplitude of each state S.F. is probability that state  B is produced in reaction. This is the quantity that is compared to structure theory

31. Single Particle Transfer at Intermediate Energies (3) Radioactive beam experiments are often conducted at intermediate energies and in inverse kinematics. Forward focused beam and reaction products; difficult to get elastic scattering measurement on composite target (like “d”).

32. Eikonal Model [6] Knockout Reactions create many-body final states with: –removal (stripping) of the nucleon by deuteron breakup –elastic breakup (diffraction dissociation) of the projectile [6] P.G. Hansen and J.A. Tostevin, Annu. Rev. Nucl. Part. Sci. 53 (2003) 219

33. Background Single particle states are strong if particle is transferred to nucleus. Single particle states are strong if particle is transferred to nucleus. Single hole states are strong if particle is removed from nucleus. Single hole states are strong if particle is removed from nucleus. 48 Ca( 7 Li, 6 He) 49 Sc K.W. Kemper et al. Nucl. Phys. A348, 339 (1980) 5.09 MeV 4.49 MeV 3.08 MeV G.S. 50 Ti(d, 3 He) 49 Sc P. Doll et al. J. Phys. G, Vol. 5, No. 10, 1421 (1979). 2.23 MeV 2.36 MeV 4.01 MeV

34. One-neutron knockout on N=16 nuclei Counts/11 keV.. ef B(E2 )( ef m) 24 DSAM [7] (p,p )[ 9], Coulomb ex.[ 10] Present wor k Nakada et al.[ 8] ee l. [93] Ot suka et al.[ 94] Brown [103] Primary beam 36 Ar (150 MeV/nucleon) Primary target: 9 Be (1034 mg/cm 2 ) Knockout target: 9 Be (188 mg/cm 2 ) 34 Ar @ 70 MeV/nucleon (mid- target) 33 Cl @ 66 MeV/nucleon 32 S @ 63 MeV/nucleon Particle ID with S800 Momentum reconstruction with S800 γ -ray spectroscopy with SeGA … primary beam 31 Ar 32 Ar 33 Ar 34 Ar 35 K 33 Cl 32 Cl 31 Cl one-neutron knockout N=16  N=15 31 S 29 S 32 S 33 S 30 S 35 Ar 34 Cl 35 Cl 34 S 36 Ar N=15

35. more than 50MeV/nucleon: sudden approximation + eikonal approach Spectroscopic Factors determined from the population of the residue with A-1 Spectroscopy of the wave function: One-nucleon knockout ),(),()( 2 j nsp BjInjSCnI   diffrstrip ),(),(),( nspn n BjBjBj    P.G. Hansen and B.M. Sherrill, Nucl. Phys. A 693, 133 (2001). P.G. Hansen and J. A. Tostevin, Annu. Phys. Rev. Nucl. Part. Sci., in press nuclear structure information reaction process residue moment distribution  -value of knocked-out n

36. Inclusive momentum distributions Counts/11 keV.. ef B(E2 )( ef m) 24 DSAM [7] (p,p )[ 9], Coulomb ex.[ 10] Present wor k Nakada et al.[ 8] ee l. [93] Ot suka et al.[ 94] Brown [103] 11.6 100 11.011.411.2 200 0 Counts / 16.7MeV/c P || (GeV/c) knockout residues Fragment momentum distribution (longitudinal): depends on angular momentum ( -value) of the knocked-out neutron Inclusive momentum distribution: contains all particles  superposition of excited-state and ground-state momentum distribution -value assigned in comparison to model calculations (black-disk approximation) =0 =2 P.G. Hansen, PRL 77, 1016 (1996)

37. Momentum distributions for the knockout to individual final states Counts/11 keV. N=8 d 5/2 s 1/2 excited final state of 33 Ar ground state of 33 Ar = 2 = 0 in coincidence with γ- rays knockout residues without γ -ray A. Gade et al., PRC 69 034311(2004) 34 Ar

38. γ -ray spectroscopy to tag the final state Counts/11 keV S p =3340(30) keV 1358(5) keV 1795(7) keV 0.0 keV 3818(11) keV (5/2 + ) 3/2 + 5/2 + 1/2 + 4047.8 keV 1847.6 keV 1431.6 keV 3/2 + 5/2 + (level scheme confirmed by PhD thesis of R.R.C. Clement, MSU 2003) BR (%)  exp (mb) C 2 S exp 1/2 + 30.2(46) 4.7(9) 0.38(6) 3/2 + 20.2(44) 3.2(8) 0.36(9) 5/2 + 31.7(31) 4.9(7) 0.56(8) (5/2 + ) 17.9(30) 2.8(6)>0.34(7) A. Gade et al., PRC 69 034311 (2004)

39. Adiabatic Model Calcs. [2] [4] J.A. Tostevin, M. Igarashi, et al. – Computer Program “TWOFNR” [5] W.D. Metz et al. Phys. Rev. C Vol. 12, #3 (1975) 827 [3] K.W. Kemper et al. Nucl. Phys. A348 (1980) 339

40. Highly selected references- Direct Nuclear References G. R. Satchler, Oxford Science Publications 1983 Study of the (d,p) reaction in the 1p shell J. P. Schiffer et al Phys. Rev.164, 1274 (1967) Systematic extraction of spectroscopic factors from 12 C(d,p) and 13 C(p,d) reactions X. D. Liu et al Phys. Rev. C69, 064313 (2004) Comprehensive analysis method for (d,p) stripping reactions N. Keeley et al Phys. Rev. C69, 064604 (2004)

41. This is a wonderful time to be in nuclear physics In the next ten years there will be new accelerators being commissioned There will be new detector systems and computing capabilities will continue to increase so that we don’t know what discoveries will be made, just that there will be some