1 / 23

Sizes

Gross Properties of Nuclei. Sizes. Nuclear Sizes. Absorption upon intersection of nuclear cross section area s

savannah-gomez
Télécharger la présentation

Sizes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Gross Properties of Nuclei Sizes Nuclear Sizes

  2. Absorption upon intersection of nuclear cross section area s jbeam current areal densityA area illuminated by beamL = 6.022 1023/mol Loschmidt# NT # target nuclei in beamMT target molar weightrT target densitydx target thickness [s]=1barn = 10-24cm2 Absorption Probability and Cross Section Mass absorption coefficient m: dN = -Nm dx Transmitted Incoming Illuminated area A dx Nucleus cross section area sT Thin target, thickness x  Target/Absorber Nuclear Sizes elementary absorption cross section area per nucleus

  3. Cntr Amp/Disc Size Information from Nuclear Scattering (Pu-Be) n Source Basic exptl. setup with n source: Count Target in/target out Target n Detector Electronics DAQ d from small accelerator (Ed100 keV): T(d,n)3He En 14 MeV Experiment (approx. analysis) Nuclear Sizes J.B.A. England, Techn.Nucl. Str. Meas., Halsted, New York,1974 Equilibrium matter density r0

  4. q d Interaction Radii a scattering 16O scattering 12C scattering D.D. Kerlee et al., PR 107, 1343 (1957) Nuclear Sizes Distance of closest approach  scatter angle q P.R. Christensen et al., NPA207, 33 (1973)

  5. b a Elastic Electron Scattering Simplified treatment: Incoming plane wave= approximation to particle wave packet. Independent nucleons, impulse approximation. Detector l l Elementary scattering waves arrive at detector with phase differences  calculate relative to nuclear center Nuclear Sizes probability amplitude for proton n

  6. Momentum Transfer and Scatter Angle in (e,e’) For given energy, scattering angle q determines momentum transfer. Controllable by experiment (E, q). <bra* | ket> Carry out integration over r, rn’ except rn Nuclear Sizes =f0 x density of proton n at rn

  7. Separation of Variables Point nucleus (PN): a=b, jn=0  determine scaling factor Z protons Finite nucleus: integrate over space where proton wave function are non-zero Strength of Coulomb interaction same for each proton Nuclear Sizes Scatter cross section for finite nucleus = cross section for point-nucleus x form factor F of charge distribution

  8. Mott Cross Section for Electron Scattering In typical nuclear applications, electron kinetic energies K » mec2 (extreme) relativistic domain (b =v/c) check non-relativistic limit e- = good probe for objects on fm scale Nuclear Sizes Obtained in 1. order quantum mechanical perturbation theory, neglects nuclear recoil momentum.

  9. Elastic (e,e) Scattering Data ds/dW diffraction patterns1st. minimum q(q)4.5/R 3-arm electron spectrometer (Univ. Mainz) X 10 Nuclear Sizes X 0.1 R. Hofstadter, Electron Scattering and Nuclear Structure, Benjamin, 1963 J.B. Bellicard et al., PRL 19,527 (1967)

  10. r r R Fourier Transform of Charge Distribution Form factor F contains entire information about charge distribution R Generic Fourier transform of f: 4.4a C Nuclear Sizes Fermi distribution r, half-density radius C diffuseness a C is different from the radius of equivalent sharp sphere Req

  11. Nuclear Charge Form Factor Form factor for Coulomb scattering = Fourier transform of charge distribution. Nuclear Sizes

  12. r r R Model-Independent Analysis of Scattering Interpretation in terms of radial moments of charge distributionExpansion: =1 Nuclear Sizes mean-square radius of charge distribution Equivalent sharp radius of any r(r):

  13. t=4.4a Nuclear Charge Distributions (e,e) Rz(H) = (0.85-0.87) fmRz(He)= 1.67 fm C: Half-density radiusa: Surface diffusenesst: Surface thickness Leptodermous: t « C Holodermous : t ~ C Nuclear Sizes Density of 4He is 2 x r0 ! R. Hofstadter, Ann. Rev. Nucl. Sci. 7, 231 (1957)

  14. Charge Radius Systematics Note: Slightly different fit line, if not forced through zero. Nuclear Sizes r0(charge) decreases for heavy nuclei like Z/A  for all nuclei: r0(mass) = 0.17 fm-3 = const.  1014 g/cm3 (r0=1.07 fm)

  15. r(r) point nucleus r(r) r Excited ground nuclear state Muonic X-Rays Effect exists for also for e-atoms but is weaker than for muonsNegative muon:m- e- mm = 207me Replace electron by muon  “muonic atom” Bohr orbits, am = ae/207 107 times stronger fields • X-ray energies 100keV–6 MeV • Isomeric/isotopic shifts DEis VCoul(r) En r 3d2p 1s DEis(2p) Finite size Nuclear Sizes DEis(1s) Point Nucleus

  16. Energy/keV Charge Radii from Muonic Atoms 2p3/2 1s1/2 2p1/2 1s1/2 2p3/2 1s1/2 Nuclear Sizes 2p1/2 1s1/2 Engfer et al., Atomic Nucl. Data Tables 14, 509 (1974) R(A) sensitive to isotopic, isomeric, chemical effects. Adding n dilutes rZ(r) E.B. Shera et al., PRC14, 731 (1976)

  17. Mass and Charge Distributions Parameters of Fermi Distribution Charge density: Mass density distribution scales: except for small surface increase in n density (“neutron skin”) Constant central density for all nuclides, except the very light (Li, Be, B,..) Nuclear Sizes

  18. Leptodermous Distributions R.W. Hasse & W.D. Myers, Geometrical relationships of macroscopic nuclear physics, Springer V., New York, 1988 Fermi Distribution (a C) C = Central radiusR = Equivalent sharp radiusQ = Equivalent rms radiusb= Surface width Leptodermous Expansion in (b/R)n Nuclear Sizes

  19. Studies with Secondary Beams Produce a secondary beam of projectiles from interactions of intense primary beam with “production” target  projectiles rare/unstable isotopes, induce scattering and reactions in “p” target Nuclear Sizes Tanihata et al., RIKEN-AF-NP-233 (1996)

  20. “Interaction Radii for Exotic Nuclei Derive sR =sTotal - selastic sR =:p[RI(P)+RI(T)]2 Nuclear Sizes Kox Parameterization: Interaction Radius =(N-Z)/2 Tanihata et al., RIKEN-AF-NP-168 (1995)

  21. n 9Li 11Li n “Halo” Nuclei From p scattering on 11Li  extended mass distribution (“halo”). Valence-neutron correlations in 11Li: r1 = r2 = 5 fm, r12 = 7 fm Parameterization: tn 6He - 8He mass density distributions Experiment: dashed, Theory (fit):solid Nuclear Sizes Korshenninikov et al., RIKEN-AF-NP-233, 1996

  22. n n 4He Neutron Skin of Exotic (n-Rich) Nuclei Which n Orbits? Qrms (4He) = (1.57±0.05)fm Qrms (6He) = (2.48±0.03)fm Qrms (8He) = (2.52±0.03)fmV(8He) = 4.1 x V(4He) ! rms matter radii Tanihata et al., PLB 289,261 (1992) Thick n-skin for light n-rich nuclei: tn≈ 0.9 fm (6He, 8He) DRrms =Rnrms - Rprms Relativistic mean field calculations: tn eF Plausible because of weaker nuclear force 133Cs78 stable, normal n-skin thickness, tn ~0.1fm181Cs126 unstable, significant n-skin, tn ~ 2 fm Can one actually make 181Cs, role of outer n ?? Nuclear Sizes Are there p-halos ?  Not yet known. D.H. Hirata et al., PRC 44, 1467(1991)

  23. End of Nuclear Sizes Nuclear Sizes

More Related