687:
when the two electrons are dipolar coupled, another mechanism occurs: the cross-effect. In that case, the DNP process is the result of irradiation of an allowed transition (called single quantum) as a result the strength of microwave irradiation is less demanded than that in the solid effect. In practice, the correct EPR frequency separation is accomplished through random orientation of paramagnetic species with g-anisotropy. Since the "frequency" distance between the two electrons should be equal to the Larmor frequency of the targeted nucleus, cross-effect can only occur if the inhomogeneously broadened EPR lineshape has a linewidth broader than the nuclear Larmor frequency. Therefore, as this linewidth is proportional to external magnetic field B
720:
interactions. The strong interactions lead to a homogeneously broadened EPR lineshape of the involved paramagnetic species. The linewidth is optimized for polarization transfer from electrons to nuclei, when it is close to the nuclear Larmor frequency. The optimization is related to an embedded three-spin (electron-electron-nucleus) process that mutually flips the coupled three spins under the energy conservation (mainly) of the Zeeman interactions. Due to the inhomogeneous component of the associated EPR lineshape, the DNP enhancement by this mechanism also scales as B
695:. This remains true as long as the relaxation times remain constant. Usually going to higher field leads to longer nuclear relaxation times and this may partially compensate for the line broadening reduction. In practice, in a glassy sample, the probability of having two dipolarly coupled electrons separated by the Larmor frequency is very scarce. Nonetheless, this mechanism is so efficient that it can be experimentally observed alone or in addition to the solid-effect.
756:. Such electrons can give large polarization enhancements to nearby protons via proton-proton spin-diffusion if they are not so close together that the electron-nuclear dipolar interaction does not broaden the proton resonance beyond detection. For small isolated clusters, the free electrons are fixed and give rise to solid-state enhancements (SS). The maximal proton solid-state enhancement is observed at microwave offsets of ω ≈ ω
704:
multi-step process involving EPR single quantum transition, electron dipolar anti-crossing and cross effect degeneracy conditions. In the most simple case the MAS-DNP mechanism can be explained by the combination of a single quantum transition followed by the cross-effect degeneracy condition, or by the electron-dipolar anti-crossing followed by the cross-effect degeneracy condition.
733:
660:
the exciting microwave frequency shifts up or down by the nuclear Larmor frequency from the electron Larmor frequency in the discussed two-spin system. The direction of frequency shifts corresponds to the sign of DNP enhancements. Solid effect exist in most cases but is more easily observed if the linewidth of the EPR spectrum of involved
784:= 0. The cellulose char also exhibits electrons undergoing thermal mixing effects (TM). While the enhancement curve reveals the types electron-nuclear spin interactions in a material, it is not quantitative and the relative abundance of the different types of nuclei cannot be determined directly from the curve.
103:, because of the lack of microwave (or terahertz) sources operating at the appropriate frequency. Today such sources are available as turn-key instruments, making DNP a valuable and indispensable method especially in the field of structure determination by high-resolution solid-state NMR spectroscopy.
672:
In the case of magic angle spinning DNP (MAS-DNP), the mechanism is different but to understand it, a two spins system can still be used. The polarization process of the nucleus still occurs when the microwave irradiation excites the double quantum or zero quantum transition, but due to the fact that
659:
when all the relaxation parameters are kept constant. Once this transition is excited and the relaxation is acting, the magnetization is spread over the "bulk" nuclei (the major part of the detected nuclei in an NMR experiment) via the nuclear dipole network. This polarizing mechanism is optimal when
120:
level populations observed in metals and free radicals when electron spin transitions are saturated by microwave irradiation. This effect relies on stochastic interactions between an electron and a nucleus. The "dynamic" initially meant to highlight the time-dependent and random interactions in this
744:
Many types of solid materials can exhibit more than one mechanism for DNP. Some examples are carbonaceous materials such bituminous coal and charcoal (wood or cellulose heated at high temperatures above their decomposition point which leaves a residual solid char). To separate out the mechanisms of
703:
As in the static case, the MAS-DNP mechanism of cross effect is deeply modified due to the time dependent energy level. By taking a simple three spin system, it has been demonstrated that the cross-effect mechanism is different in the Static and MAS case. The cross effect is the result of very fast
650:
In a simple picture of an electron-nucleus two-spin system, the solid effect occurs when a transition involving an electron-nucleus mutual flip (called zero quantum or double quantum) is excited by a microwave irradiation, in the presence of relaxation. This kind of transition is in general weakly
809:
is transferred onto the nuclear spins of interest using a microwave source. There are two main DNP approaches for solids. If the material does not contain suitable unpaired electrons, exogenous DNP is applied: the material is impregnated by a solution containing a specific radical. When possible,
686:
The cross effect requires two unpaired electrons as the source of high polarization. Without special condition, such a three spins system can only generate a solid effect type of polarization. However, when the resonance frequency of each electron is separated by the nuclear Larmor frequency, and
79:
When electron spin polarization deviates from its thermal equilibrium value, polarization transfers between electrons and nuclei can occur spontaneously through electron-nuclear cross relaxation or spin-state mixing among electrons and nuclei. For example, the polarization transfer is spontaneous
651:
allowed, meaning that the transition moment for the above microwave excitation results from a second-order effect of the electron-nuclear interactions and thus requires stronger microwave power to be significant, and its intensity is decreased by an increase of the external magnetic field B
719:
Thermal mixing is an energy exchange phenomenon between the electron spin ensemble and the nuclear spin, which can be thought of as using multiple electron spins to provide hyper-nuclear polarization. Note that the electron spin ensemble acts as a whole because of stronger inter-electron
607:, resulting in a loss of the electron polarization. In addition, due to the small state mixing caused by the B term of the hyperfine interaction, it is possible to irradiate on the electron-nucleus zero quantum or double quantum ("forbidden") transitions around
527:
909:
J. Puebla; E.A. Chekhovich; M. Hopkinson; P. Senellart; A. Lemaitre; M.S. Skolnick; A.I. Tartakovskii (2013). "Dynamic nuclear polarization in InGaAs/GaAs and GaAs/AlGaAs quantum dots under non-resonant ultra-low power optical excitation".
796:
signals but also to introduce an inherent spatial dependence: the magnetization enhancement takes place in the vicinity of the irradiated electrons and propagates throughout the sample. Spatial selectivity can finally be obtained using
305:
310:
These terms are referring respectively to the electron and nucleus Zeeman interaction with the external magnetic field, and the hyperfine interaction. S and I are the electron and nuclear spin operators in the Zeeman basis (spin
673:
the sample is spinning, this condition is only met for a short time at each rotor cycle (which makes it periodical). The DNP process in that case happens step by step and not continuously as in the static case.
588:
745:
DNP and to characterize the electron-nuclear interactions occurring in such solids a DNP enhancement curve can be made. A typical enhancement curve is obtained by measuring the maximum intensity of the NMR
166:
While the
Overhauser effect relies on time-dependent electron-nuclear interactions, the remaining polarizing mechanisms rely on time-independent electron-nuclear and electron-electron interactions.
801:(MRI) techniques, so that signals from similar parts can be separated based on their location in the sample. DNP has triggered enthusiasm in the NMR community because it can enhance sensitivity in
1466:
Wind, R.A.; Li, L.; Maciel, G.E.; Wooten, J.B. (1993). "Characterization of
Electron Spin Exchange Interactions in Cellulose Chars by Means of ESR, 1H NMR, and Dynamic Nuclear Polarization".
60:. It is also possible that those electrons are aligned to a higher degree of order by other preparations of electron spin order such as: chemical reactions (leading to chemical-induced DNP,
1842:
Maly, Thorsten; Debelouchina, Galia T.; Bajaj, Vikram S.; Hu, Kan-Nian; Joo, Chan-Gyu; Mak–Jurkauskas, Melody L.; Sirigiri, Jagadishwar R.; Van Der Wel, Patrick C. A.; et al. (2008).
382:
99:
The first DNP experiments were performed in the early 1950s at low magnetic fields but until recently the technique was of limited applicability for high-frequency, high-field
2118:
Dynamic
Nuclear Polarization: New Experimental and Methodology Approaches and Applications in Physics, Chemistry, Biology and Medicine, Appl. Magn. Reson., 2008. 34(3–4)
1113:
T. Maly; G.T. Debelouchina; V.S. Bajaj; K.-N. Hu; C.G. Joo; M.L. Mak-Jurkauskas; J.R. Sirigiri; P.C.A. van der Wel; J. Herzfeld; R.J. Temkin; R.G. Griffin (2008).
1172:
A.B. Barnes; G. De Paëpe; P.C.A. van der Wel; K.-N. Hu; C.G. Joo; V.S. Bajaj; M.L. Mak-Jurkauskas; J.R. Sirigiri; J. Herzfeld; R.J. Temkin; R.G. Griffin (2008).
772:
are the electron and nuclear Larmor frequencies, respectively. For larger and more densely concentrated aromatic clusters, the free electrons can undergo rapid
1410:"Theory for cross effect dynamic nuclear polarization under magic-angle spinning in solid state nuclear magnetic resonance: the importance of level crossings"
180:
2052:
Wind, R.A.; Duijvestijn, M.J.; Van Der Lugt, C.; Manenschijn, A.; Vriend, J. (1985). "Applications of dynamic nuclear polarization in C NMR in solids".
1361:
Mentink-Vigier, F.; Akbey, U.; Hovav, Y.; Vega, S.; Oschkinat, H.; Feintuch, A. (2012). "Fast passage dynamic nuclear polarization on rotating solids".
628:, resulting in polarization transfer between the electrons and the nuclei. The effective MW irradiation on these transitions is approximately given by
1342:
1914:
Barnes, A. B.; De Paëpe, G.; Van Der Wel, P. C. A.; Hu, K.-N.; Joo, C.-G.; Bajaj, V. S.; Mak-Jurkauskas, M. L.; Sirigiri, J. R.; et al. (2008).
802:
84:
chemical reaction. On the other hand, when the electron spin system is in a thermal equilibrium, the polarization transfer requires continuous
136:
and other renowned physicists of the time on the grounds of being "thermodynamically improbable". The experimental confirmation by Carver and
2082:
1832:
1758:
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848:
174:
The simplest spin system exhibiting the SE DNP mechanism is an electron-nucleus spin pair. The
Hamiltonian of the system can be written as:
2152:
532:
822:. It is important to note that DNP was only performed ex situ as it usually requires low temperature to lower electronic relaxation.
749:
of the H nuclei, for example, in the presence of continuous microwave irradiation as a function of the microwave frequency offset.
1671:
Sze, Kong Hung; Wu, Qinglin; Tse, Ho Sum; Zhu, Guang (2011). "Dynamic
Nuclear Polarization: New Methodology and Applications".
1119:
753:
89:
1996:
Nuclear
Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
866:
2101:
Anatole
Abragam and Maurice Goldman, "Nuclear Magnetism: Order and Disorder", New York : Oxford University Press, 1982
147:, which is responsible for the DNP phenomenon is caused by rotational and translational modulation of the electron-nucleus
343:
are the secular and pseudo-secular parts of the hyperfine interaction. For simplicity we will only consider the case of |
1356:
1354:
815:
69:
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793:
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Carbonaceous materials such as cellulose char contain large numbers of stable free electrons delocalized in large
2147:
93:
1076:
T.R. Carver; C.P. Slichter (1956). "Experimental
Verification of the Overhauser Nuclear Polarization Effect".
1510:
707:
This in turn change dramatically the CE dependence over the static magnetic field which does not scale like B
522:{\displaystyle H=\Delta \omega _{e}\;S_{z}+\omega _{\rm {n}}I_{z}+AS_{z}I_{z}+B\ S_{z}I_{x}+\omega _{1}S_{x}}
362:
has little effect on the evolution of the spin system. During DNP a MW irradiation is applied at a frequency
1628:
Ni, Qing Zhe; Daviso E; Can TV; Markhasin E; Jawla SK; Swager TM; Temkin RJ; Herzfeld J; Griffin RG (2013).
1339:
92:(EPR) frequency. In particular, mechanisms for the microwave-driven DNP processes are categorized into the
137:
53:
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DNP was first realized using the concept of the
Overhauser effect, which is the perturbation of nuclear
81:
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The MW irradiation can excite the electron single quantum transitions ("allowed transitions") when
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57:
45:
41:
1982:
1601:
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1250:
1004:
Solem, J. C. (1974). "Dynamic polarization of protons and deuterons in solid deuterium hydride".
947:
921:
891:
148:
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High field dynamic nuclear polarization – the renaissance, Phys. Chem. Chem. Phys., 2010. 12(22)
16:
Spin polarization of atomic nuclei in response to electron spin realignment in a magnetic field
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776:. These electrons give rise to an Overhauser enhancement centered at a microwave offset of ω
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Solem, J. C.; Rebka Jr., G. A. (1968). "EPR of atoms and radicals in radiation-damaged H
935:
879:
2098:
Carson
Jeffries, "Dynamic Nuclear Orientation", New York, Interscience Publishers, 1963
1940:
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300:{\displaystyle H_{0}=\omega _{e}S_{z}+\omega _{\rm {n}}I_{z}+AS_{z}I_{z}+B\ S_{z}I_{x}}
160:
117:
49:
140:
as well as an apologetic letter from Ramsey both reached Overhauser in the same year.
2141:
2065:
1986:
1978:
1605:
1552:
1254:
1025:
895:
887:
691:, the overall DNP efficiency (or the enhancement of nuclear polarization) scales as B
151:. The theory of this process is based essentially on the second-order time-dependent
129:
37:
2044:
1495:
951:
736:
H DNP-NMR enhancement curve for cellulose char heated for several hours at 350 °C. P
912:
1511:"Dynamic Nuclear Polarization Solid-State NMR Spectroscopy for Materials Research"
1223:"High-Temperature Dynamic Nuclear Polarization Enhanced Magic-Angle-Spinning NMR"
1589:
1304:
Carver, T.R.; Slichter, C.P. (1953). "Polarization of Nuclear Spins in Metals".
133:
2105:
2015:
1916:"High-Field Dynamic Nuclear Polarization for Solid and Solution Biological NMR"
1174:"High-Field Dynamic Nuclear Polarization for Solid and Solution Biological NMR"
943:
1931:
1906:
1383:
1306:
1270:
1238:
1189:
1039:
T.R. Carver; C.P. Slichter (1953). "Polarization of Nuclear Spins in Metals".
990:
2023:
Atsarkin, V A (1978). "Dynamic polarization of nuclei in solid dielectrics".
1957:
Abragam, A; Goldman, M (1978). "Principles of dynamic nuclear polarization".
1597:
1544:
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1326:
1246:
1062:
864:
A. Abragam; M. Goldman (1976). "Principles of Dynamic Nuclear Polarization".
1812:
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Miéville, Pascal; Jannin, Sami; Helm, Lothar; Bodenhausen, Geoffrey (2011).
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96:(OE), the solid-effect (SE), the cross-effect (CE) and thermal-mixing (TM).
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1949:
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Günther, Ulrich L. (2011). "Dynamic Nuclear Hyperpolarization in Liquids".
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1707:
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is smaller than the nuclear Larmor frequency of the corresponding nuclei.
2132:
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33:
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Bagheri, Khashayar; Deschamps, Michael; Salager, Elodie (1 April 2023).
818:. The experiments usually need to be performed at low temperatures with
1479:
1867:
1645:
1434:
1140:
732:
1571:"Nuclear magnetic resonance for interfaces in rechargeable batteries"
1708:"NMR of Insensitive Nuclei Enhanced by Dynamic Nuclear Polarization"
1222:
655:. As a result, the DNP enhancement from the solid effect scales as B
68:
and spin injection. DNP is considered one of several techniques for
926:
731:
61:
48:
are aligned. Note that the alignment of electron spins at a given
1994:
Goertz, S.T. (2004). "The dynamic nuclear polarization process".
583:{\displaystyle \Delta \omega _{e}=\omega _{e}-\omega _{\rm {MW}}}
1819:. Annual Reports on NMR Spectroscopy. Vol. 73. p. 83.
1675:. Topics in Current Chemistry. Vol. 326. pp. 215–42.
1778:"Dynamic nuclear polarization: Yesterday, today, and tomorrow"
1745:. Topics in Current Chemistry. Vol. 335. pp. 23–69.
740:– 1 is the relative polarization or intensity of the H signal.
1268:
Overhauser, A.W. (1953). "Polarization of Nuclei in Metals".
1221:
Akbey, U.; Linden, A. H. & Oschkinat, H. (May 2012).
841:
Spin Temperature and Nuclear Magnetic Resonance in Solids
814:
ions (metal-ion dynamic nuclear polarization, MIDNP) or
711:
and makes it much more efficient than the solid effect.
1844:"Dynamic nuclear polarization at high magnetic fields"
1115:"Dynamic Nuclear Polarization at High Magnetic Fields"
88:
irradiation at a frequency close to the corresponding
535:
385:
376:, resulting in a rotating frame Hamiltonian given by
335:
are the electron and nuclear Larmor frequencies, and
183:
1564:
1562:
2054:
Progress in Nuclear Magnetic Resonance Spectroscopy
810:endogenous DNP is performed using the electrons in
1578:Current Opinion in Colloid & Interface Science
1340:Purdue University Obituary of Albert W. Overhauser
582:
521:
299:
124:The DNP phenomenon was theoretically predicted by
2108:, Spindrift Publications, The Netherlands, 2016
128:in 1953 and initially drew some criticism from
1509:Moroz, Ilia B.; Leskes, Michal (1 July 2022).
2075:Hyperpolarization methods in NMR spectroscopy
1630:"High Frequency Dynamic Nuclear Polarization"
8:
2106:"Essentials of Dynamic Nuclear Polarization"
1893:Kemsley, Jyllian (2008). "Sensitizing Nmr".
1817:Solution-State Dynamic Nuclear Polarization
1712:CHIMIA International Journal for Chemistry
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1401:
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2073:Kuhn, Lars T.; et al., eds. (2013).
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1673:NMR of Proteins and Small Biomolecules
1782:Journal of Physics: Conference Series
7:
1536:10.1146/annurev-matsci-081720-085634
792:DNP can be performed to enhance the
52:and temperature is described by the
1515:Annual Review of Materials Research
1825:10.1016/B978-0-08-097074-5.00003-7
1408:Thurber, K. R.; Tycko, R. (2012).
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754:polycyclic aromatic hydrocarbons
72:. DNP can also be induced using
2045:10.1070/PU1978v021n09ABEH005678
1895:Chemical & Engineering News
1848:The Journal of Chemical Physics
1120:The Journal of Chemical Physics
1006:Nuclear Instruments and Methods
143:The so-called electron-nucleus
121:polarization transfer process.
90:electron paramagnetic resonance
1959:Reports on Progress in Physics
1803:10.1088/1742-6596/324/1/012003
867:Reports on Progress in Physics
774:electron exchange interactions
1:
1634:Accounts of Chemical Research
805:. In DNP, a large electronic
2066:10.1016/0079-6565(85)80005-4
1026:10.1016/0029-554X(74)90294-8
321:considered for simplicity),
28:) results from transferring
22:Dynamic nuclear polarization
1590:10.1016/j.cocis.2022.101675
843:. Oxford University Press.
2169:
2153:Nuclear magnetic resonance
2016:10.1016/j.nima.2004.03.147
1979:10.1088/0034-4885/41/3/002
1920:Applied Magnetic Resonance
1468:Applied Magnetic Resonance
1178:Applied Magnetic Resonance
944:10.1103/PhysRevB.88.045306
888:10.1088/0034-4885/41/3/002
799:magnetic resonance imaging
728:DNP-NMR enhancement curves
1932:10.1007/s00723-008-0129-1
1907:10.1021/cen-v086n043.p012
1384:10.1016/j.jmr.2012.08.013
1239:10.1007/s00723-012-0357-2
1190:10.1007/s00723-008-0129-1
991:10.1103/PhysRevLett.21.19
839:Goldman, Maurice (1970).
699:Magic angle spinning case
668:Magic angle spinning case
1327:10.1103/PhysRev.92.212.2
1063:10.1103/PhysRev.92.212.2
1725:10.2533/chimia.2011.260
1100:10.1103/PhysRev.102.975
971:Physical Review Letters
40:, thereby aligning the
2025:Soviet Physics Uspekhi
1776:Atsarkin, V A (2011).
1743:Modern NMR Methodology
1291:10.1103/PhysRev.92.411
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54:Boltzmann distribution
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2077:. Berlin: Springer.
1751:10.1007/128_2011_229
1681:10.1007/128_2011_297
820:magic angle spinning
816:conduction electrons
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383:
181:
157:von Neumann equation
2037:1978SvPhU..21..725A
2008:2004NIMPA.526...28G
1971:1978RPPh...41..395A
1860:2008JChPh.128e2211M
1811:Lingwood, Mark D.;
1794:2011JPhCS.324a2003A
1527:2022AnRMS..52...25M
1427:2012JChPh.137h4508T
1376:2012JMagR.224...13M
1319:1953PhRv...92..212C
1283:1953PhRv...92..411O
1133:2008JChPh.128e2211M
1092:1956PhRv..102..975C
1055:1953PhRv...92..212C
1018:1974NucIM.117..477S
983:1968PhRvL..21...19S
936:2013PhRvB..88d5306P
880:1978RPPh...41..395A
153:perturbation theory
58:thermal equilibrium
44:to the extent that
1480:10.1007/BF03162519
1345:2006-01-09 at the
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662:unpaired electrons
646:Static sample case
580:
519:
358:|. In such a case
297:
149:hyperfine coupling
74:unpaired electrons
2131:The DNP-NMR blog
2084:978-3-642-39728-8
1868:10.1063/1.2833582
1834:978-0-08-097074-5
1760:978-3-642-37990-1
1690:978-3-642-28916-3
1646:10.1021/ar300348n
1435:10.1063/1.4747449
1227:Appl. Magn. Reson
1141:10.1063/1.2833582
850:978-0-19-851251-6
807:spin polarization
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126:Albert Overhauser
112:Overhauser effect
94:Overhauser effect
70:hyperpolarization
30:spin polarization
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2104:Tom Wenckebach,
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1956:
1913:
1892:
1841:
1835:
1810:
1775:
1761:
1740:
1705:
1691:
1670:
1627:
1624:
1622:Review articles
1619:
1617:Further reading
1614:
1613:
1573:
1568:
1567:
1560:
1508:
1507:
1503:
1465:
1464:
1460:
1407:
1406:
1399:
1360:
1359:
1352:
1347:Wayback Machine
1338:
1334:
1303:
1302:
1298:
1267:
1266:
1262:
1220:
1219:
1215:
1171:
1170:
1166:
1112:
1111:
1107:
1079:Physical Review
1075:
1074:
1070:
1042:Physical Review
1038:
1037:
1033:
1003:
1002:
998:
968:
964:
963:
959:
908:
907:
903:
863:
862:
858:
851:
838:
837:
833:
828:
803:solid-state NMR
790:
783:
779:
771:
767:
763:
759:
739:
730:
723:
717:
710:
701:
694:
690:
684:
679:
670:
658:
654:
648:
641:
634:
627:
620:
613:
606:
599:
565:
552:
539:
531:
530:
509:
499:
486:
476:
457:
447:
431:
419:
406:
395:
381:
380:
375:
368:
357:
334:
326:
317:
313:
312:
287:
277:
258:
248:
232:
220:
207:
197:
184:
179:
178:
172:
114:
109:
66:optical pumping
17:
12:
11:
5:
2166:
2164:
2156:
2155:
2150:
2140:
2139:
2136:
2135:
2127:
2124:
2123:
2122:
2119:
2114:
2113:Special issues
2111:
2110:
2109:
2102:
2099:
2094:
2091:
2090:
2089:
2083:
2070:
2049:
2031:(9): 725–745.
2020:
2002:(1–2): 28–42.
1991:
1954:
1911:
1890:
1839:
1833:
1808:
1773:
1759:
1738:
1718:(4): 260–263.
1703:
1689:
1668:
1640:(9): 1933–41.
1623:
1620:
1618:
1615:
1612:
1611:
1558:
1501:
1474:(2): 161–176.
1458:
1415:J. Chem. Phys.
1397:
1364:J. Mag. Reson.
1350:
1332:
1313:(1): 212–213.
1296:
1277:(2): 411–415.
1260:
1233:(1–2): 81–90.
1213:
1164:
1105:
1086:(4): 975–980.
1068:
1049:(1): 212–213.
1031:
1012:(2): 477–485.
996:
966:
957:
901:
874:(3): 395–467.
856:
849:
830:
829:
827:
824:
789:
786:
781:
777:
769:
765:
761:
757:
737:
729:
726:
721:
716:
715:Thermal mixing
713:
708:
700:
697:
692:
688:
683:
680:
678:
675:
669:
666:
656:
652:
647:
644:
639:
632:
625:
618:
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604:
597:
591:
590:
576:
573:
568:
564:
559:
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516:
512:
506:
502:
498:
493:
489:
483:
479:
472:
469:
464:
460:
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450:
446:
443:
438:
434:
427:
422:
418:
413:
409:
402:
398:
394:
391:
388:
373:
369:and intensity
366:
355:
332:
324:
308:
307:
294:
290:
284:
280:
273:
270:
265:
261:
255:
251:
247:
244:
239:
235:
228:
223:
219:
214:
210:
204:
200:
196:
191:
187:
171:
168:
161:density matrix
113:
110:
108:
105:
50:magnetic field
46:electron spins
15:
13:
10:
9:
6:
4:
3:
2:
2165:
2154:
2151:
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2100:
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2038:
2034:
2030:
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2013:
2009:
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1980:
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1972:
1968:
1964:
1960:
1955:
1951:
1947:
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1933:
1929:
1925:
1921:
1917:
1912:
1908:
1904:
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1900:
1896:
1891:
1887:
1883:
1878:
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1869:
1865:
1861:
1857:
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1849:
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1840:
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1826:
1822:
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1791:
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1756:
1752:
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1469:
1462:
1459:
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1440:
1436:
1432:
1428:
1424:
1421:(8): 084508.
1420:
1417:
1416:
1411:
1404:
1402:
1398:
1393:
1389:
1385:
1381:
1377:
1373:
1369:
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1365:
1357:
1355:
1351:
1348:
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1341:
1336:
1333:
1328:
1324:
1320:
1316:
1312:
1309:
1308:
1300:
1297:
1292:
1288:
1284:
1280:
1276:
1273:
1272:
1264:
1261:
1256:
1252:
1248:
1244:
1240:
1236:
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1200:
1195:
1191:
1187:
1183:
1179:
1175:
1168:
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1156:
1151:
1146:
1142:
1138:
1134:
1130:
1126:
1122:
1121:
1116:
1109:
1106:
1101:
1097:
1093:
1089:
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1081:
1080:
1072:
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1043:
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1032:
1027:
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1011:
1007:
1000:
997:
992:
988:
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980:
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972:
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937:
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893:
889:
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868:
860:
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852:
846:
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832:
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817:
813:
808:
804:
800:
795:
787:
785:
775:
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750:
748:
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727:
725:
714:
712:
705:
698:
696:
681:
676:
674:
667:
665:
663:
645:
643:
638:
631:
624:
617:
610:
603:
596:
566:
562:
557:
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540:
514:
510:
504:
500:
496:
491:
487:
481:
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350:
346:
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271:
268:
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253:
249:
245:
242:
237:
233:
221:
217:
212:
208:
202:
198:
194:
189:
185:
177:
176:
175:
169:
167:
164:
162:
159:for the spin
158:
154:
150:
146:
141:
139:
135:
131:
130:Norman Ramsey
127:
122:
119:
111:
106:
104:
102:
97:
95:
91:
87:
83:
77:
75:
71:
67:
63:
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42:nuclear spins
39:
38:atomic nuclei
35:
31:
27:
23:
19:
2074:
2057:
2053:
2028:
2024:
1999:
1995:
1962:
1958:
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1367:
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682:Static case
134:Felix Bloch
2142:Categories
1965:(3): 395.
1813:Han, Songi
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1307:Phys. Rev.
1271:Phys. Rev.
826:References
351:|<<|
107:Mechanisms
56:under the
2060:: 33–67.
1987:250855406
1606:255364390
1598:1359-0294
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2033:Bibcode
2004:Bibcode
1967:Bibcode
1941:2634864
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1444:3443114
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1279:Bibcode
1199:2634864
1150:2770872
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1088:Bibcode
1051:Bibcode
1014:Bibcode
979:Bibcode
932:Bibcode
876:Bibcode
788:DNP-NMR
316:⁄
2133:(Link)
2081:
1985:
1948:
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2093:Books
1983:S2CID
1602:S2CID
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1549:S2CID
1492:S2CID
1251:S2CID
948:S2CID
922:arXiv
892:S2CID
768:and ω
62:CIDNP
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2079:ISBN
1946:PMID
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