Abstract
Nuclei are experimentally observed to have charge radii that show remarkably different trends to those that may be naively expected from liquid drop or droplet behavior. Instead, its variation with proton and neutron numbers exhibits diverse patterns that offer a unique insight into the structure of atomic nuclei and fundamental symmetries. The techniques developed to measure nuclear charge radii during the last 50–70 years have become increasingly sensitive and are nowadays applied to determine differential changes throughout the nuclear landscape from the lightest to the heaviest elements. While elastic electron scattering and muonic-atom spectroscopy has been applied almost exclusively to stable isotopes, optical and particularly laser spectroscopy has become a unique tool to gain insight into the behavior of nuclear charge radii along isotopic chains of short-lived isotopes. Collinear laser spectroscopy and resonance ionization spectroscopy are the workhorses for these studies and have already been applied to a significant fraction of the nuclear chart. This chapter will provide an overview on the techniques that are used to determine nuclear charge radii and a selection of results from different regions of the nuclear chart to highlight some of the unique phenomena exhibited by this fundamental property.
References
S.A. Ahmad et al., Mean square charge radii of radium isotopes and octupole deformation in the 220−228Ra region. Nucl. Phys. A 483, 244–268 (1988). https://doi.org/10.1016/0370-2693(83)90103-X
G.D. Alkhazov et al., Measurement of isotropic variations in the charge radii of europium nuclei by the method of three-stepped laser photoionization of atoms. JETP Lett. 37, 274 (1983). https://jetpletters.ru/ps/1492/article_22784.shtml
G.D. Alkhazov et al., A new highly efficient method of atomic spectroscopy for nuclides far from stability. Nucl. Instrum. Methods Phys. Res. Sect. B 69, 517–520 (1992). https://doi.org/10.1016/0168-583X(92)95309-F
R.V. Ambartsumyan, V.N. Kalinin, V.S. Letokhov, Two-step selective photoionization of rubidium atoms by laser radiation. JETP Lett. 13, 217–219 (1971)
I. Angeli, K.P. Marinova, Correlations of nuclear charge radii with other nuclear observables. J. Phys. G 42, 055108 (2015). https://doi.org/10.1088/0954-3899/42/5/055108
A. Antognini et al., Proton structure from the measurement of 2S-2P transition frequencies of muonic hydrogen. Science 339, 417–420 (2013). https://doi.org/10.1126/science.1230016
A. Antognini et al., Measurement of the quadrupole moment of 185Re and 187Re from the hyperfine structure of muonic X rays. Phys. Rev. C 101, 054313 (2020). https://doi.org/10.1103/PhysRevC.101.054313
K.-R. Anton et al., Collinear laser spectroscopy on fast atomic beams. Phys. Rev. Lett. 40, 642–645 (1978). https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.40.642
J. Ärje et al., Submillisecond on-line mass separation of nonvolatile radioactive elements: an application of charge exchange and thermalization processes of primary recoil ions in helium. Phys. Rev. Lett. 54, 99–101 (1985). https://doi.org/10.1103/PhysRevLett.54.99
H. Backe, W. Lauth, M. Block, M. Laatiaoui, Prospects for laser spectroscopy, ion chemistry and mobility measurements of superheavy elements in buffer-gas traps. Nucl. Phys. A 944, 492–517 (2015). https://doi.org/10.1016/j.nuclphysa.2015.07.002
H. Backe et al., Isotope shift measurements for superdeformed fission isomeric states. Phys. Rev. Lett. 80, 920–923 (1998). https://doi.org/10.1103/PhysRevLett.80.920
H. Backe et al., Isotope shift measurement at 244fAm. Hyperfine Interact. 127, 35–39 (2000). https://doi.org/10.1023/A:1012690022283
F. Barranco, R.A. Broglia, Correlation between mean square radii and zero-point motions of the surface in the Ca isotopes. Phys. Lett. B 151, 90–94 (1985). https://doi.org/10.1016/0370-2693(85)91391-7
R.C. Barrett, Model-independent parameters of the nuclear charge distribution from muonic X-rays. Phys. Lett. B 33, 388–390 (1970). https://doi.org/10.1016/0370-2693(70)90611-8
A. Barzakh et al., Large shape staggering in neutron-deficient Bi isotopes. Phys. Rev. Lett. 127, 192501 (2021). https://doi.org/10.1103/PhysRevLett.127.192501
M.A. Belushkin, H.-W. Hammer, U.-G. Meißner, Dispersion analysis of the nucleon form factors including meson continua. Phys. Rev. C 75 (2007). https://doi.org/10.1103/PhysRevC.75.035202
J.C. Berengut et al., Probing new long-range interactions by isotope shift spectroscopy. Phys. Rev. Lett. 120, 091801 (2018). https://doi.org/10.1103/PhysRevLett.120.091801
J.C. Bernauer et al., High-precision determination of the electric and magnetic form factors of the proton. Phys. Rev. Lett. 105, 242001 (2010). https://doi.org/10.1103/PhysRevLett.105.242001
A. Beyer et al., The rydberg constant and proton size from atomic hydrogen. Science 358, 79–85 (2017). https://doi.org/10.1126/science.aah6677
N. Bezginov et al., A measurement of the atomic hydrogen Lamb shift and the proton charge radius. Science 365, 1007–1012 (2019). https://doi.org/10.1126/science.aau7807
K. Blaum et al., A novel scheme for a highly selective laser ion source. Nucl. Instrum. Methods Phys. Res. Sect. B 204, 331–335 (2003). https://doi.org/10.1016/S0168-583X(02)01942-0
M. Block, Heaviest Elements – Decay and Laser Spectroscopy, in Nuclear Physics Handbook (Springer, New York, 2023)
M. Block, M. Laatiaoui, S. Raeder, Recent progress in laser spectroscopy of the actinides. Prog. Part. Nucl. Phys. 116, 103834 (2021). https://doi.org/10.1016/j.ppnp.2020.103834
J. Bonn et al., Sudden change in the nuclear charge distribution of very light mercury isotopes. Phys. Lett. B 38, 308–311 (1972). https://doi.org/10.1016/0370-2693(72)90253-5
W. Borchers, R. Neugart, E.W. Otten, H.T. Duong, G. Ulm, K. Wendt, Hyperfine structure and isotope shift investigations in 202−222Rn for the study of nuclear structure beyond Z = 82. Hyperfine Interact. 34, 25–29 (1987). https://doi.org/10.1007/BF02072676
W. Borchers et al., Xenon isotopes far from stability studied by collisional ionization laser spectroscopy. Phys. Lett. B 216, 7–10 (1989). https://doi.org/10.1016/0370-2693(89)91359-2
S. Bourzeix et al., High resolution spectroscopy of the hydrogen atom: Determination of the 1S Lamb shift. Phys. Rev. Lett. 76(3), 384–387 (1996). ISSN 0031-9007. https://doi.org/10.1103/PhysRevLett.76.384
C. Brandau et al., Precise determination of the 2s1∕2 − 2p1∕2 splitting in very heavy lithiumlike ions utilizing dielectronic recombination. Phys. Rev. Lett. 91, 073202 (2003). https://doi.org/10.1103/PhysRevLett.91.073202
C. Brandau et al., Isotope shift in the dielectronic recombination of three-electron ANd57+. Phys. Rev. Lett. 100, 073201 (2008). https://doi.org/10.1103/PhysRevLett.100.073201
B.H. Bransden, C.J. Joachain, Physics of Atoms and Molecules (Prentice Hall, 2003). ISBN 9780582356924
F. Buchinger et al., Systematics of nuclear ground state properties in 78−100Sr by laser spectroscopy. Phys. Rev. C 41, 2883–2897 (1990). https://doi.org/10.1103/PhysRevC.41.2883
P.A. Butler et al., Evolution of octupole deformation in radium nuclei from coulomb excitation of radioactive 222Ra and 228Ra beams. Phys. Rev. Lett. 124, 042503 (2020). https://doi.org/10.1103/PhysRevLett.124.042503
R.B. Cakirli, R.F. Casten, K. Blaum, Correlations of experimental isotope shifts with spectroscopic and mass observables. Phys. Rev. C 82, 061306 (2010). https://doi.org/10.1103/PhysRevC.82.061306
P. Campbell et al., Laser spectroscopy of cooled zirconium fission fragments. Phys. Rev. Lett. 89, 082501 (2002). https://doi.org/10.1103/PhysRevLett.89.082501
Y. Cao et al., Landscape of pear-shaped even-even nuclei. Phys. Rev. C 102, 024311 (2020). https://doi.org/10.1103/PhysRevC.102.024311
R.F. Casten., NpNn systematics in heavy nuclei. Nucl. Phys. A 443, 1–28 (1985). https://doi.org/10.1016/0375-9474(85)90318-5
E. Caurier et al., Shell model description of isotope shifts in calcium. Phys. Lett. B 522, 240–244 (2001). https://doi.org/10.1016/S0370-2693(01)01246-1
F.C. Charlwood et al., Nuclear charge radii of molybdenum fission fragments. Phys. Lett. B 674, 23–27 (2009). https://doi.org/10.1016/j.physletb.2009.02.050
B. Cheal, T.E. Cocolios, S. Fritzsche, Laser spectroscopy of radioactive isotopes: role and limitations of accurate isotope-shift calculations. Phys. Rev. A 86, 042501 (2012). https://doi.org/10.1103/PhysRevA.86.042501
B. Cheal et al., The shape transition in the neutron-rich yttrium isotopes and isomers. Phys. Lett. B 645, 133–137 (2007). https://doi.org/10.1016/j.physletb.2006.12.053
B. Cheal et al., Laser spectroscopy of niobium fission fragments: first use of optical pumping in an ion beam cooler buncher. Phys. Rev. Lett. 102, 222501 (2009). https://doi.org/10.1103/PhysRevLett.102.222501
P. Chhetri et al., Precision measurement of the first ionization potential of nobelium. Phys. Rev. Lett. 120, 263003 (2018). https://doi.org/10.1103/PhysRevLett.120.263003
H. Choi et al., In-gas-cell laser ionization spectroscopy of 194, 196Os isotopes by using a multireflection time-of-flight mass spectrograph. Phys. Rev. C 102, 034309 (2020). https://doi.org/10.1103/PhysRevC.102.034309
C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions (Wiley, New York, 1998). ISBN 0471293369
R.P. de Groote et al., Dipole and quadrupole moments of 73–78Cu as a test of the robustness of the Z = 28 shell closure near 78Ni. Phys. Rev. C 96, 041302 (2017). https://doi.org/10.1103/PhysRevC.96.041302
R.P. de Groote et al., Measurement and microscopic description of odd–even staggering of charge radii of exotic copper isotopes. Nat. Phys. 16, 620–624 (2020). https://doi.org/10.1038/s41567-020-0868-y
H. De Witte et al., Nuclear charge radii of neutron-deficient lead isotopes beyond N = 104 midshell investigated by in-source laser spectroscopy. Phys. Rev. Lett. 98, 112502 (2007) https://doi.org/10.1103/PhysRevLett.98.112502
H. DeVries, C.W. DeJager, C. DeVries, Nuclear charge-density-distribution parameters from elastic electron-scattering. Atomic Data Nucl. Data Tables 36, 495–536 (1987). https://doi.org/10.1016/0092-640X(87)90013-1
G.W.F. Drake, High-precision calculations for the Rydberg states of helium, in Long-Range Casimir Forces: Theory and Recent Experiments on Atomic Systems, ed. by F.S. Levin, D.A. Micha (Springer, Boston, 1993), pp. 107–217. https://doi.org/10.1007/978-1-4899-1228-2_3
B. Dreher et al., The determination of the nuclear ground state and transition charge density from measured electron scattering data. Nucl. Phys. A 235, 219–248 (1974). https://doi.org/10.1016/0375-9474(74)90189-4
H.T. Duong et al., Shape transition in neutron deficient Pt isotopes. Phys. Lett. B 217, 401–405 (1989). https://doi.org/10.1016/0370-2693(89)90068-3
Dynamic Properties, Nuclear Physics Handbook (Springer, New York, 2023)
D.A. Eastham et al., Coincidence laser spectroscopy – a new ultrasensitive technique for fast ionic or atomic-beams. Opt. Commun. 60, 293–295 (1986). https://doi.org/10.1016/0030-4018(86)90153-7
S. Eliseev et al., Phase-imaging ion-cyclotron-resonance measurements for short-lived nuclides. Phys. Rev. Lett. 110, 082501 (2013). https://doi.org/10.1103/PhysRevLett.110.082501
J. Engel et al., Time-reversal violating Schiff moment of 225Ra. Phys. Rev. C 68, 025501 (2003). https://doi.org/10.1103/PhysRevC.68.025501
J. Erler et al., Weak polarized electron scattering. Ann. Rev. Nucl. Part. Sci. 64(1), 269–298 (2014). https://doi.org/10.1146/annurev-nucl-102313-025520
G. Ewald et al., Nuclear charge radii of 8, 9Li determined by laser spectroscopy. Phys. Rev. Lett. 93, 113002 (2004). https://doi.org/10.1103/physrevlett.93.113002
G.J. Farooq-Smith et al., Laser and decay spectroscopy of the short-lived isotope 214Fr in the vicinity of the N = 126 shell closure. Phys. Rev. C 94, 054305 (2016). https://doi.org/10.1103/PhysRevC.94.054305
V.N. Fedoseyev et al., Atomic lines isotope shifts of short-lived radioactive Eu studied by high-sensitive laser resonance photoionization method in on-line experiments with proton beams. Opt. Commun. 52, 24–28 (1984). https://doi.org/10.1016/0030-4018(84)90067-1
V.N. Fedosseev, Y. Kudryavtsev, V.I. Mishin, Resonance laser ionization of atoms for nuclear physics. Phys. Scr. 85, 058104 (2012). https://doi.org/10.1088/0031-8949/85/05/058104
V.N. Fedosseev et al., Atomic spectroscopy studies of short-lived isotopes and nuclear isomer separation with the ISOLDE RILIS. Nucl. Instrum. Methods Phys. Res. Sect. B 204, 353–358 (2003). https://doi.org/10.1016/S0168-583X(02)01959-6
R. Ferrer et al., Towards high-resolution laser ionization spectroscopy of the heaviest elements in supersonic gas jet expansion. Nat. Commun. 8, 14520 (2017). https://doi.org/10.1038/ncomms14520
R. Ferrer et al., Hypersonic nozzle for laser-spectroscopy studies at 17 K characterized by resonance-ionization-spectroscopy-based flow mapping. Phys. Rev. Res. 3, 043041 (2021). https://doi.org/10.1103/PhysRevResearch.3.043041
D.A. Fink et al., In-source laser spectroscopy with the laser ion source and trap: first direct study of the ground-state properties of 217, 219Po. Phys. Rev. X 5, 011018 (2015). https://doi.org/10.1103/PhysRevX.5.011018
H. Fleurbaey et al., New measurement of the 1S-3S transition frequency of hydrogen: contribution to the proton charge radius puzzle. Phys. Rev. Lett. 120, 183001 (2018). https://doi.org/10.1103/PhysRevLett.120.183001
J.L. Friar, J.W. Negele, Theoretical and experimental determination of nuclear charge distributions, in Advances in Nuclear Physics, ed. by M. Baranger, E. Vogt, vol. 8 (Springer, Boston, 1975), pp. 219–376. https://doi.org/10.1007/978-1-4757-4398-2_3
J.L. Friar, J. Martorell, D.W.L. Sprung, Nuclear sizes and the isotope shift. Phys. Rev. A 56, 4579–4586 (1997). https://doi.org/10.1103/PhysRevA.56.4579
G. Fricke, K. Heilig, Nuclear Charge Radii. Elementary Particles, Nuclei and Atoms, vol. 20 (Springer, Berlin/Heidelberg, 2004)
G. Fricke et al., Nuclear ground state charge radii from electromagnetic interactions. Atomic Data Nucl. Data Tables 60, 177–285 (1995). https://doi.org/10.1006/adnd.1995.1007
L.P. Gaffney et al., Studies of pear-shaped nuclei using accelerated radioactive beams. Nature 497, 199–204 (2013). https://doi.org/10.1038/nature12073
H. Gao, M. Vanderhaeghen, The proton charge radius. Rev. Mod. Phys. 94 (2022). ISSN 0034-6861. https://doi.org/10.1103/RevModPhys.94.015002
J.E. García-Ramos, K. Heyde, Subtle connection between shape coexistence and quantum phase transition: the Zr case. Phys. Rev. C 102, 054333 (2020). https://doi.org/10.1103/PhysRevC.102.054333
R.F. Garcia Ruiz et al., Development of a sensitive setup for laser spectroscopy studies of very exotic calcium isotopes. J. Phys. G 44, 044003 (2017). https://doi.org/10.1088/1361-6471/aa5a24
R.F. Garcia Ruiz et al., Spectroscopy of short-lived radioactive molecules. Nature 581, 396–400 (2020). https://doi.org/10.1038/s41586-020-2299-4
P.E. Garrett, M. Zielińska, E. Clément, An experimental view on shape coexistence in nuclei. Prog. Part. Nucl. Phys. 103931 (2021). https://doi.org/10.1016/j.ppnp.2021.103931
H. Geiger, E. Marsden, On the scattering of the α-particles by matter. Proc. R. Soc. Lond. A 81(546), 174–177 (1908). https://doi.org/10.1098/rspa.1908.0067
H. Geiger, E. Marsden, On a diffuse reflection of the α-particles. Proc. R. Soc. Lond. A 82(557), 495–500 (1909). https://doi.org/10.1098/rspa.1909.0054
H. Geiger, E. Marsden, The scattering of α-particles by matter. Proc. R. Soc. Lond. A 83(565), 492–504 (1910). https://doi.org/10.1098/rspa.1910.0038
R.J. Glauber, Theory of high energy hadron-nucleus collisions, in High-Energy Physics and Nuclear Structure, ed. by S. Devons (Springer, Boston, 1970), pp. 207–264. https://doi.org/10.1007/978-1-4684-1827-9_43
P.M. Goddard, P.D. Stevenson, A. Rios, Charge radius isotope shift across the N = 126 shell gap. Phys. Rev. Lett. 110, 032503 (2013). https://doi.org/10.1103/PhysRevLett.110.032503
C. Gorges et al., Isotope shift of 40, 42, 44, 48Ca in the 4s2S1∕2 → 4p2P3∕2 transition. J. Phys. B 48, 245008 (2015). https://doi.org/10.1088/0953-4075/48/24/245008
C. Gorges et al., Laser spectroscopy of neutron-rich tin isotopes: a discontinuity in charge radii across the N = 82 shell closure. Phys. Rev. Lett. 122, 192502 (2019). https://doi.org/10.1103/PhysRevLett.122.192502
C. Granados et al., In-gas laser ionization and spectroscopy of actinium isotopes near the N = 126 closed shell. Phys. Rev. C 96, 054331 (2017). https://doi.org/10.1103/PhysRevC.96.054331
A. Grinin et al., Two-photon frequency comb spectroscopy of atomic hydrogen. Science 370, 1061–1066 (2020). https://doi.org/10.1126/science.abc7776
G. Hagen et al., Neutron and weak-charge distributions of the 48Ca nucleus. Nat. Phys. 12, 186–190 (2016). https://doi.org/10.1038/nphys3529
L.N. Hand, D.G. Miller, R. Wilson, Electric and magnetic form factors of the nucleon. Rev. Mod. Phys. 35(2), 335–349 (1963). https://doi.org/10.1103/RevModPhys.35.335
R. Heinke et al., High-resolution in-source laser spectroscopy in perpendicular geometry. Hyperfine Interact. 238, 6 (2016). https://doi.org/10.1007/s10751-016-1386-2
K. Heyde, J.L. Wood, Shape coexistence in atomic nuclei. Rev. Mod. Phys. 83, 1467–1521 (2011). https://doi.org/10.1103/RevModPhys.83.1467
T. Hilberath, S. Becker, G. Bollen, H.J. Kluge, U. Krönert, G. Passler, J. Rikovska, R. Wyss, Ground-state properties of neutron-deficient platinum isotopes. Zeitschrift für Physik A 342, 1–15 (1992). https://doi.org/10.1007/BF01294481
Y. Hirayama et al., Doughnut-shaped gas cell for KEK Isotope Separation System. Nucl. Instrum. Methods Phys. Res. Sect. B 412, 11–18 (2017). https://doi.org/10.1016/j.nimb.2017.08.037
G.S. Hurst, M.G. Payne, Principles and Applications of Resonance Ionzation Spectroscopy (Hilger, Bristol, 1988)
R.L. Jaffe, Ambiguities in the definition of local spatial densities in light hadrons. Phys. Rev. D 103 (2021). https://doi.org/10.1103/PhysRevD.103.016017
J.A. Jansen, R.T. Peerdeman, C. de Vries, Nuclear charge radii of 12C and 9Be. Nucl. Phys. A 188, 337–352 (1972)
R. Kanungo et al., Proton distribution radii of 12−19C illuminate features of neutron halos. Phys. Rev. Lett. 117, 102501 (2016)
J.-P. Karr, D. Marchand, E. Voutier, The proton size. Nat. Rev. Phys. 2, 601–614 (2020). https://doi.org/10.1038/s42254-020-0229-x
S.L. Kaufman, High-resolution laser spectroscopy in fast beams. Opt. Commun. 17, 309–312 (1976). https://doi.org/10.1016/0030-4018(76)90267-4
M. Keim et al., Laser-spectroscopy measurements of 72−96Kr spins, moments and charge radii . Nucl. Phys. A 586, 219–239 (1995). https://doi.org/10.1016/0375-9474(94)00786-M
W.H. King, Isotope Shifts in Atomic Spectra. Physics of Atoms and Molecules Series (Springer, New York, 1984). ISBN 9781489917867
A. Klose et al., Tests of atomic charge-exchange cells for collinear laser spectroscopy. Nucl. Instrum. Methods Phys. Res. Sect. A 678, 114–121 (2012). https://doi.org/10.1016/j.nima.2012.03.006
K. König et al., A new collinear apparatus for laser spectroscopy and applied science (COALA). Rev. Sci. Instrum. 91, 081301 (2020). https://doi.org/10.1063/5.0010903
K. König et al., Beam energy determination via collinear laser spectroscopy. Phys. Rev. A 103 (2021). https://doi.org/10.1103/PhysRevA.103.032806
H. Kopferman, Nuclear Moments, 2nd edn. (Elsevier Science, Burlington, 1958). ISBN 9781483230610
M. Kortelainen et al., Universal trend of charge radii of even-even Ca–Zn nuclei. Phys. Rev. C 105 (2022). https://doi.org/10.1103/PhysRevC.105.L021303
Á. Koszorús et al., Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character of N = 32. Nat. Phys. 17, 439–443 (2021). https://doi.org/10.1038/s41567-020-01136-5
J.J. Krauth et al., Measuring the α-particle charge radius with muonic helium-4 ions. Nature 589, 527–531 (2021). https://doi.org/10.1038/s41586-021-03183-1
A. Krieger et al., Calibration of the isolde acceleration voltage using a high-precision voltage divider and applying collinear fast beam laser spectroscopy. Nucl. Instrum. Methods Phys. Res. A 632, 23–31 (2011). https://doi.org/10.1016/j.nima.2010.12.145
A. Krieger et al., Nuclear charge radius of 12Be. Phys. Rev. Lett. 108, 142501 (2012). https://doi.org/10.1103/PhysRevLett.108.142501
A. Krieger et al., Frequency-comb referenced collinear laser spectroscopy of Be+ for nuclear structure investigations and many-body QED tests. Appl. Phys. B 123, 15 (2017). https://doi.org/10.1007/s00340-016-6579-5
T. Kron et al., Hyperfine structure study of 97, 98, 99Tc in a new laser ion source for high-resolution laser spectroscopy. Phys. Rev. C 102, 034307 (2020). https://doi.org/10.1103/PhysRevC.102.034307
U. Krönert et al., Resonance lonization mass spectroscopy with a pulsed thermal atomic beam. Appl. Phys. A 44, 339–345 (1987). https://doi.org/10.1007/BF00624601
Y.A. Kudriavtsev, V.S. Letokhov, Laser method of highly selective detection of rare radioactive isotopes through multistep photoionization of accelerated atoms. Appl. Phys. B 29, 219–221 (1982). https://doi.org/10.1007/BF00688671
Y. Kudryavtsev et al., Dual chamber laser ion source at LISOL. Nucl. Instrum. Methods Phys. Res. Sect. B 267, 2908–2917 (2009). https://doi.org/10.1016/j.nimb.2009.06.013
M. Laatiaoui et al., Atom-at-a-time laser resonance ionization spectroscopy of nobelium. Nature 538, 495–498 (2016). https://doi.org/10.1038/nature19345
J. Lee et al., Charge-radius changes in even-A platinum nuclei. Phys. Rev. C 38, 2985–2988 (1988). https://doi.org/10.1103/PhysRevC.38.2985
J.K.P. Lee et al., Resonant ionization spectroscopy of laser-desorbed gold isotopes. AIP Conf. Proc. 164, 205 (1987). https://doi.org/10.1063/1.37034
M. Lestinsky et al., Physics book: CRYRING@ESR. Eur. Phys. J. – Spec. Top. 225, 797–882 (2016). https://doi.org/10.1140/epjst/e2016-02643-6
V.S. Letokhov, Laser Photoionization Spectroscopy (Academic, Orlando, 1987)
P. Lievens et al., Nuclear ground state properties of 99Sr by collinear laser spectroscopy with non-optical detection. Phys. Lett. B 256, 141–145 (1991). https://doi.org/10.1016/0370-2693(91)90664-C
Y.-H. Lin, H.-W. Hammer, U.-G. Meißner, High-precision determination of the electric and magnetic radius of the proton. Phys. Lett. B 816, 136254 (2021). https://doi.org/10.1016/j.physletb.2021.136254
Z.-T. Lu, K. Wendt, Laser-based methods for ultrasensitive trace-isotope analyses. Rev. Sci. Instrum. 74, 1169 (2003). https://doi.org/10.1063/1.1535232
Z.T. Lu et al., Colloquium: laser probing of neutron-rich nuclei in light atoms. Rev. Mod. Phys. 85, 1383–1400 (2013). https://doi.org/10.1103/RevModPhys.85.1383
K.M. Lynch et al., Decay-assisted laser spectroscopy of neutron-deficient francium. Phys. Rev. X 4, 011055 (2014). https://doi.org/10.1103/PhysRevX.4.011055
B. Maaß et al., Towards laser spectroscopy of the proton-halo candidate 8B. Hyperfine Interact. 238, 25 (2017). https://doi.org/10.1007/s10751-017-1399-5
B. Maaß et al., Nuclear charge radii of 10, 11B. Phys. Rev. Lett. 122, 182501 (2019). https://doi.org/10.1103/PhysRevLett.122.182501
S. Malbrunot-Ettenauer et al., Nuclear charge radii of the nickel isotopes 58−68, 70Ni. Phys. Rev. Lett. 128, 022502 (2022). https://doi.org/10.1103/PhysRevLett.128.022502
B.A. Marsh et al., Characterization of the shape-staggering effect in mercury nuclei. Nat. Phys. 14, 1163–1167 (2018). https://doi.org/10.1038/s41567-018-0292-8
A.J. Miller et al., Proton superfluidity and charge radii in proton-rich calcium isotopes. Nat. Phys. 15, 432–436 (2019). https://doi.org/10.1038/s41567-019-0416-9
G.A. Miller, Defining the proton radius: a unified treatment. Phys. Rev. C, 99, 035202 (2019). https://doi.org/10.1103/PhysRevC.99.035202
P.J. Mohr, D.B. Newell, B.N. Taylor, CODATA recommended values of the fundamental physical constants: 2014. Rev. Mod. Phys. 88, 035009 (2016). https://doi.org/10.1103/RevModPhys.88.035009
A.C. Mueller et al., Spins, moments and charge radii of barium isotopes in the range 122−146Ba determined by collinear fast-beam laser spectroscopy. Nucl. Phys. A 403, 234–262 (1983). https://doi.org/10.1016/0375-9474(83)90226-9
M. Mukai et al., In-gas-cell laser resonance ionization spectroscopy of 196, 197, 198Ir. Phys. Rev. C 102, 054307 (2020). https://doi.org/10.1103/PhysRevC.102.054307
P. Müller et al., Nuclear charge radius of 8He. Phys. Rev. Lett. 99, 252501 (2007). https://doi.org/10.1103/PhysRevLett.99.252501
W.D. Myers, W.J. Swiatecki, Average nuclear properties. Ann. Phys. 55, 395–505 (1969). https://doi.org/10.1016/0003-4916(69)90202-4
A. Navin et al., Direct evidence for the breakdown of the N = 8 shell closure in 12Be. Phys. Rev. Lett. 85, 266–269 (2000). https://doi.org/10.1103/PhysRevLett.85.266
R. Neugart, W. Klempt, K. Wendt, Collisional ionization as a sensitive detection scheme in collinear laser-fast-beam spectroscopy. Nucl. Instrum. Methods Phys. Res. B 17, 354–359 (1986). https://doi.org/10.1016/0168-583X(86)90125-4
R. Neugart et al., Precision measurement of 11Li moments: influence of halo neutrons on the 9Li core. Phys. Rev. Lett. 101, 132502 (2008). https://doi.org/10.1103/PhysRevLett.101.132502
G. Neyens, R.P. de Groote, Spins and electromagnetic moments of nuclei, in Nuclear Physics Handbook (Springer, New York, 2023)
A. Nieminen et al., On-line ion cooling and bunching for collinear laser spectroscopy. Phys. Rev. Lett. 88, 094801 (2002). https://doi.org/10.1103/PhysRevLett.88.094801
NIST, 2018 codata recommended values (2022). https://physics.nist.gov/cgi-bin/cuu/Value?rp|search_for=proton+radius
W. Nörtershäuser et al., Nuclear charge radii of 7, 9, 10Be and the one-neutron halo nucleus 11Be. Phys. Rev. Lett. 102, 062503 (2009). https://doi.org/10.1103/Physrevlett.102.062503
W. Nörtershäuser et al., Isotope-shift measurements of stable and short-lived lithium isotopes for nuclear-charge-radii determination. Phys. Rev. A 83, 012516 (2011a). https://doi.org/10.1103/PhysRevA.83.012516
W. Nörtershäuser et al., Charge radii and ground state structure of lithium isotopes: experiment and theory reexamined. Phys. Rev. C 84, 024307 (2011b). https://doi.org/10.1103/PhysRevC.84.024307
G. Papadimitriou et al., Charge radii and neutron correlations in helium halo nuclei. Phys. Rev. C 84, 051304 (2011). https://doi.org/10.1103/PhysRevC.84.051304
C.G. Parthey et al., Improved measurement of the hydrogen 1S-2S transition frequency. Phys. Rev. Lett. 107, 203001 (2011). https://doi.org/10.1103/PhysRevLett.107.203001
V. Patkóš, V.A. Yerokhin, K. Pachucki, Complete α7m Lamb shift of helium triplet states. Phys. Rev. A 103 (2021). https://doi.org/10.1103/PhysRevA.103.042809
U.C. Perera, A.V. Afanasjev, P. Ring, Charge radii in covariant density functional theory: a global view. Phys. Rev. C 104 (2021). https://doi.org/10.1103/PhysRevC.104.064313
R. Pohl et al., The size of the proton. Nature 466, 213–216 (2010). https://doi.org/10.1038/nature09250
R. Pohl, R. Gilman, G.A. Miller, K. Pachucki, Muonic hydrogen and the proton radius puzzle. Annu. Rev. Nucl. Part. Sci. 63, 175–204 (2013). https://doi.org/10.1146/annurev-nucl-102212-170627
R. Pohl et al., Laser spectroscopy of muonic deuterium. Science 353, 669–673 (2016). https://doi.org/10.1126/science.aaf2468
E. Pollard, Nuclear potential barriers: experiment and theory. Phys. Rev. 47, 611–620 (1935). https://doi.org/10.1103/PhysRev.47.611
M. Puchalski, A.M. Moro, K. Pachucki, Isotope shift of the 32S1∕2-22S1∕2 transition in lithium and the nuclear polarizability. Phys. Rev. Lett. 97, 133001 (2006). https://doi.org/10.1103/PhysRevLett.97.133001
M. Puchalski, K. Pachucki, J. Komasa, Isotope shift in a beryllium atom. Phys. Rev. A 89, 012506 (2014). https://doi.org/10.1103/PhysRevA.89.012506
S. Raeder et al., Probing sizes and shapes of nobelium isotopes by laser spectroscopy. Phys. Rev. Lett. 120, 232503 (2018). https://doi.org/10.1103/PhysRevLett.120.232503
P.G. Reinhard, D. Drechsel, Ground state correlations and the nuclear charge distribution. Zeitschrift für Physik A 290, 85–91 (1979). https://doi.org/10.1007/BF01408483
P.G. Reinhard, W. Nazarewicz, Toward a global description of nuclear charge radii: exploring the Fayans energy density functional. Phys. Rev. C 95, 064328 (2017). https://doi.org/10.1103/PhysRevC.95.064328
M. Reponen et al., Evidence of a sudden increase in the nuclear size of proton-rich silver-96. Nat. Commun. 12, 4596 (2021). https://doi.org/10.1038/s41467-021-24888-x
L.M. Robledo, R. Rodríguez-Guzmán, P. Sarriguren, Role of triaxiality in the ground-state shape of neutron-rich Yb, Hf, W, Os and Pt isotopes. J. Phys. G 36, 115104 (2009). https://doi.org/10.1088/0954-3899/36/11/115104
R. Rodríguez-Guzmán, P. Sarriguren, L.M. Robledo, S. Perez-Martin, Charge radii and structural evolution in Sr, Zr, and Mo isotopes. Phys. Lett. B 691, 202–207 (2010). https://doi.org/10.1016/j.physletb.2010.06.035
E. Rutherford, LXXIX. The scattering of α and β particles by matter and the structure of the atom. Lond. Edinb. Dublin Philos. Mag. J. Sci. 21(125), 669–688 (1911). ISSN 1941-5982. https://doi.org/10.1080/14786440508637080
R.G. Sachs, High-energy behavior of nucleon electromagnetic form factors. Phys. Rev. 126, 2256–2260 (1962). https://doi.org/10.1103/PhysRev.126.2256
R. Sánchez et al., Nuclear charge radius of 11Li: the influence of halo neutrons. Phys. Rev. Lett. 96, 033002 (2006). https://doi.org/10.1103/PhysRevLett.96.033002
J. Sauvage et al., COMPLIS experiments: collaboration for spectroscopy measurements using a pulsed laser ion source. Hyperfine Interact 129, 303–317 (2000). https://doi.org/10.1023/A:1012618001695
B. Schinzler et al., Collinear laser spectroscopy of neutron-rich Cs isotopes at an on-line mass separator. Phys. Lett. B 79, 209–212 (1978). https://doi.org/10.1016/0370-2693(78)90224-1
C. Schulz et al., Resonance ionization spectroscopy on a fast atomic ytterbium beam. J. Phys. B 24, 4831 (1991). https://doi.org/10.1088/0953-4075/24/22/020
C. Schwob et al., Optical frequency measurement of the 2S−12D transitions in hydrogen and deuterium: Rydberg constant and lamb shift determinations. Phys. Rev. Lett. 82, 4960–4963 (1999). https://doi.org/10.1103/PhysRevLett.82.4960
S. Sels et al., Shape staggering of midshell mercury isotopes from in-source laser spectroscopy compared with density-functional-theory and Monte Carlo shell-model calculations. Phys. Rev. C 99, 044306 (2019). https://doi.org/10.1103/PhysRevC.99.044306
E.C. Seltzer, K X-ray isotope shifts. Phys. Rev. 188, 1916–1919 (1969). https://doi.org/10.1103/PhysRev.188.1916
C. Shi et al., Unexpectedly large difference of the electron density at the nucleus in the 4p2P1∕2,3∕2 fine-structure doublet of Ca+. Appl. Phys. B 123, 2 (2016). https://doi.org/10.1007/s00340-016-6572-z
N.B. Shulgina, B. Jonson, M.V. Zhukov, 11Li structure from experimental data. Nucl. Phys. A 825, 175–199 (2009). https://doi.org/10.1016/j.nuclphysa.2009.04.014
I. Sick, Model-independent nuclear charge densities from elastic electron scattering. Nucl. Phys. A 218, 509–541 (1974). https://doi.org/10.1016/0375-9474(74)90039-6
I. Sick, Precise root-mean-square radius of 4He. Phys. Rev. C 77, 041302(R) (2008). https://doi.org/10.1103/Physrevc.77.041302
R. Silverans, G. Borghs, P. de Bisschop, M. van Hove, Fast ion beam collinear laser spectroscopy: some aspects of recent applications, sensitivity and resolution. Hyperfine Interact. 24, 181–201 (1985). https://doi.org/10.1007/BF02354811
R.E. Silverans, P. Lievens, L. Vermeeren, A sensitive measuring scheme in collinear fast-ion-beam laser spectroscopy – the optical-pumping, state-selective neutralization and particle-detection sequence. Nucl. Instrum. Methods Phys. Res. B 26, 591–597 (1987). https://doi.org/10.1016/0168-583X(87)90548-9
G.G. Simon et al., Absolute electron-proton cross sections at low momentum transfer measured with a high pressure gas target system. Nucl. Phys. A 333(3), 381–391 (1980). https://doi.org/10.1016/0375-9474(80)90104-9
F. Sommer et al., Charge radii of 55, 56Ni reveal a surprisingly similar behavior at N = 28 in Ca and Ni isotopes. Phys. Rev. Lett. 129, 132501 (2022). https://doi.org/10.1103/PhysRevLett.129.132501
P. Strasser, T. Matsuzaki, K. Nagamine, Challenge towards muonic atom formation with unstable nuclei. Eur. Phys. J. A 13, 197–202 (2002). https://doi.org/10.1140/epja1339-47
I. Talmi, On the odd-even effect in the charge radii of isotopes. Nucl. Phys. A 423, 189–196 (1984). https://doi.org/10.1016/0375-9474(84)90587-
C. Thibault et al., Hyperfine structure and isotope shift of the D2 line of 118−145Cs and some of their isomers. Nucl. Phys. A 367, 1–12 (1981a). https://doi.org/10.1016/0375-9474(81)90274-8
C. Thibault et al., Hyperfine structure and isotope shift of the D2 line of 76−98Rb and some of their isomers. Phys. Rev. C 23, 2720–2729 (1981b). https://doi.org/10.1103/PhysRevC.23.2720
T. Udem et al., Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain. Phys. Rev. Lett. 79, 2646–2649 (1997). https://doi.org/10.1103/PhysRevLett.79.2646
G. Ulm et al., Isotope shift of 182Hg and an update of nuclear moments and charge radii in the isotope range 181Hg-206Hg. Zeitschrift für Physik A 325, 247–259 (1986). https://doi.org/10.1007/BF01294605
P. Van Duppen et al., A laser ion source for on-line mass separation. Hyperfine Interact. 74, 193–204 (1992). https://doi.org/10.1007/BF02398629
L. Vermeeren et al., The mean square nuclear charge radius of 39Ca. J. Phys. G 22, 1517–1520 (1996). https://doi.org/10.1088/0954-3899/22/10/014
A.R. Vernon et al., Simulation of the relative atomic populations of elements 1 ≤ Z ≤89 following charge exchange tested with collinear resonance ionization spectroscopy of indium. Spectrochim. Acta Part B 153, 61–83 (2019). https://doi.org/10.1016/j.sab.2019.02.001
E. Verstraelen et al., Search for octupole-deformed actinium isotopes using resonance ionization spectroscopy. Phys. Rev. C 100, 044321 (2019). https://doi.org/10.1103/PhysRevC.100.044321
A. Voss et al., First use of high-frequency intensity modulation of narrow-linewidth laser light and its application in determination of 206, 205, 204Fr ground-state properties. Phys. Rev. Lett. 111, 122501 (2013). https://doi.org/10.1103/PhysRevLett.111.122501
A. Voss et al., Nuclear moments and charge radii of neutron-deficient francium isotopes and isomers. Phys. Rev. C 91, 044307 (2015). https://doi.org/10.1103/PhysRevC.91.044307
L.-B. Wang et al., Laser spectroscopic determination of the 6He nuclear charge radius. Phys. Rev. Lett. 93, 142501 (2004). https://doi.org/10.1103/PhysRevLett.93.142501
F. Wauters, A. Knecht, The muX project. SciPost Phys. Proc. 22 (2021). https://doi.org/10.21468/SciPostPhysProc.5.022
K. Wendt et al., Rapid trace analysis of 89, 90Sr in environmental samples by collinear laser resonance ionization mass spectrometry. Radiochim. Acta 79, 183 (1997). https://doi.org/10.1524/ract.1997.79.3.183
W.H. Wing, G.A. Ruff, W.E. Lamb JR., J.J. Spezeski, Observation of the infrared spectrum of the hydrogen molecular ion HD+. Phys. Rev. Lett. 36, 1488–1491 (1976). https://doi.org/10.1103/PhysRevLett.36.1488
W. Xiong et al., A small proton charge radius from an electron–proton scattering experiment. Nature 575, 147–150 (2019). https://doi.org/10.1038/s41586-019-1721-2
Z.-C. Yan, G.W.F. Drake, Lithium isotope shifts as a measure of nuclear size. Phys. Rev. A 61, 022504 (2000). https://doi.org/10.1103/PhysRevA.61.022504
D.T. Yordanov et al., Nuclear charge radii of 21−32Mg. Phys. Rev. Lett. 108, 042504 (2012). https://doi.org/10.1103/PhysRevLett.108.042504
D.T. Yordanov et al., Simple nuclear structure in 111−129Cd from atomic isomer shifts. Phys. Rev. Lett. 116, 032501 (2016). https://doi.org/10.1103/PhysRevLett.116.032501
L. Zamick, Two body contribution to the effective radius operator. Ann. Phys. 66, 784–789 (1971). https://doi.org/10.1016/0003-4916(71)90080-7
P.A. Zyla et al., Review of particle physics. Prog. Theor. Exp. Phys. 2020, 083C01 (2020). https://doi.org/10.1093/ptep/ptaa104
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2023 Springer Nature Singapore Pte Ltd.
About this entry
Cite this entry
Nörtershäuser, W., Moore, I.D. (2023). Nuclear Charge Radii. In: Tanihata, I., Toki, H., Kajino, T. (eds) Handbook of Nuclear Physics . Springer, Singapore. https://doi.org/10.1007/978-981-15-8818-1_41-1
Download citation
DOI: https://doi.org/10.1007/978-981-15-8818-1_41-1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-8818-1
Online ISBN: 978-981-15-8818-1
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics