Nuclear Spectroscopy I Augusto O. Macchiavelli Nuclear Science Division Lawrence Berkeley National Laboratory Many thanks to Rod Clark, I.Y. Lee, and Dirk Weisshaar Work supported under contract number DE-AC0-05CH1131.
Atomic nuclei constitute unique many body systems of strongly interacting fermions. Their properties and structure, are of paramount importance to many aspects of physics. Many of the phenomena encountered in nuclei share common basic physics ingredients with other mesoscopic systems, thus making nuclear structure research relevant to other areas of contemporary research, for example in condensed matter and atomic physics. These are exciting times in the field of physics of nuclei: Existing and planned exotic beam facilities worldwide and new detector systems with increased sensitivity and resolving power not only will allow us to answer some important questions we have today, but most likely will open up a window to new and unexpected phenomena. New developments in theory and computer power are shaping a path to a predictive theory of nuclei and reactions.
Proton drip-line Mirror symmetry p and p tunneling Spin triplet superconductivity (T=0 pairing) Heavy Elements Shell stability Island of SHE rp-process Novae, X-ray bursts Proton number Z Unknown nuclei Neutron number N Neutron drip-line Halos, Skins Pairing at low density New shell structure New collective modes r-process Stars, Supernovae
Outline Short Introduction Shell model and residual interactions Pairing and deformation Nilsson model Rotational motion γ-ray Spectroscopy Interactions of gamma-rays with matter Scintillators Ge detectors Compton-suppression Resolving power
Shell structure Energy of First Excited State Z N
Nuclear shell model In principle if the form of the bare nucleon-nucleon interaction is known, then the properties and structures of a given nucleus can be calculated ab-initio: + 3-body In the shell model we make the following approximations to the problem: Mean Field Residual Interaction, V(1,)
The average potential U(r k ), experienced by all the k particles approximates the combined effects of all the two-body interactions. U(r k ) = W (r k,r l ) l We now consider the motion of the valence nucleons ( i.e. neutrons or protons that are in excess of the last, completely filled shell) in the mean field and the effect of a residual interaction, V(r 1, r ), only among them. H = H core + H 1 0 + H 0 + V (1,) Problem #1
The Mean Field ω 0 41 A 1/ 3 MeV spin orbit 0 A /3 MeV V(r) / r l term 0.1MeV
The residual interaction Derive from the nn interaction with in-medium effects Determine the residual interaction from experimental data. Use a schematic model with a simple spatial form that captures the main ingredients of the force.
V(1, ) Gδ(θ 1 )+V P (θ 1 ) Short-range (Pairing ) + long-range (Quadrupole) G 0MeV / A V 50MeV / A
Pair gaps from mass differences The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. BM Vol 1 page 170
Problem #1 V(1, ) Gδ(θ 1 )+V P (θ 1 )
R 4 = E 4 E Major ingredient is V πν Federman, Pittel, Phys. Rev. C 0, 80 89 (1979) Scaling of nuclei properties with N n N p I. Hamamoto, Nucl. Phys. 73 (1965) 5. R. Casten, Phys. Lett. 15B (1985) 145.
V(β) vibrations N rotations β 0 β
Nuclear Deforma:on Problem # Residual quadrupole interac:on between nucleons outside closed shells which gives addi:onal B.E. if nuclei deform. Experimental observa:on of large electric quadrupole moments and low- lying rota:onal bands suggests nuclei can be deformed. The general shape of a nucleus can be expressed as an expansion of spherical harmonics:
Nuclear Shapes λ= is the most important term and describes quadrupole deformations. Requiring the intrinsic axes of the nucleus to coincide with the principal axes of the co-ordinate system means that α 1 =α -1 =0, and α =α -, and the nuclear deformation can be described using only two parameters α 0, α. We define: a γ = β cos 0 a = 1 β sin γ β is a measure of the quadrupole deformation, while γ is a measure of the degree of triaxiality. By convention (the Lund convention): β>0, γ=0 o is axially symmetric prolate deformation β<0, γ=-60 o is axially symmetric oblate deformation
Nilsson Model Anisotropic harmonic oscillator poten:al ( ) 3 1 1 ) ( Dl C z y x m r V + + = l.s ω ω ω If axial symmetry is presumed: 3 1 ω ω ω = An elonga:on parameter, ε, is introduced such that: = ε ω ω 3 1 0 3 + = = ε ω ω ω 3 1 1 0 1 0 3 1 ) ( ω ω ω ε = Without spin- orbit and l term the Nilsson energy levels are given by: + = + + + + + = 3 3 1 1 1 3 0 3 3 1 1 N n N n n n E ε ω ω ω ω!!!! In addi:on to the principal oscillator number N and its component n 3 the Nilsson quantum numbers are Λ=l z, Σ=s z, Ω=Λ+Σ=j z and parity π=(- 1) l. Nilsson levels are labeled: [Nn 3 Λ]Ω π Ben Mottelson, Phys. Scr. T15 (006)
Nilsson Diagram The effects of deforma:on can be seen in the diagram. Each spherical level labeled by N(l j ) at ε=0, is split into (j+1)/ levels with Ω = ± 1, ± 3,..., ± j. The remaining degeneracy means that each level can accommodate two nucleons. Orbits with lower Ω are shi\ed downwards for ε>0 (prolate) and upwards for ε<0 (oblate). Problem #4 Deformed Mean Field
A note on deforma:ons
Nuclear Rota:on The nucleus rotates as a whole. (collective degrees of freedom) Lab I The nucleons move independently inside the deformed potential (intrinsic degrees of freedom) Intrinsic The nucleonic motion is much faster than the rotation (adiabatic approximation) E E in + E rot Ψ Ψ in (x ν )Ψ rot (ψ,θ,ϕ) Φ K Ψ rot (ψ,θ,ϕ) Ψ I + = 8π 1/ 1 (,, ) D I ψ θ φ MK Φ K E E in + I(I +1) K I +...
E(I, K) = E K + AI(I +1)+ B(I(I +1))
Rotational properties: Moment of Inertia E I I(I +1) < i' j I = 1 i > e(i) e(i') = I rigid i occ,i' I rigid = " 5 MR $ 1+ 1 # 3 ε +... % ' & Correlated two particle states have much less angular momentum than the corresponding free particle motion è quasi-particles Migdal Formula: # 1 I I rigid % $ 1+ x & ( ' 3/ x = Δ D D!( ω ω 3 )!ω 0 ε
E + 3! I Irrotational flow ε Problem #3
Pair gaps from rotational properties 1 A - 1/
Quenching of Pairing correlations? ~ I I rigid Δ D ~ I ( I rigid 3 ) Mottelson and Valatin
Coriolis effects Problem #5 E(MeV) jι/j Δ ~ (I j) I + Δ ~ I I I Stephens and Simon I
World view of rare isotope facili:es ARIEL From Brad Sherrill - MSU Black produc:on in target Magenta in- flight produc:on
How to study exo:c nuclei? An ar:st view Coulomb Excitation Transfer, Deep Inelastic, Incomplete Fusion Fusion- Evaporation Fragmentation
Gamma-ray Spectroscopy and Nuclear Physics Gamma-ray spectroscopy has played a major role in the study of the atomic nucleus. Coincidence relations à Level/decay scheme Angular distributions /correlations à Multipolarity, spins Linear polarization à E/M, parity Doppler shifts à Lifetimes, B(E/M λ)
What can we infer from the γ-ray spectra? Level Schemes Contain Structural Information Collective Rotation Single Particle Alignment
Coexistence of Excitations Normal-Deformed Rotational Bands (β~0.3) Super-Deformed Rotational Bands (β~0.6)
Which detectors should we use? Effective Energy resolution (δe), Efficiency (ε), Peak-to-Background (P/T) Resolving Power GRETINA $ 0 M