{ "cells": [ { "cell_type": "markdown", "id": "19e014f7", "metadata": {}, "source": [ "# Paramagnetic Relaxation Enhancement" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "id": "a79b634b", "metadata": {}, "source": [ "Stochastic motion can modulate the Hamiltonian, leading to magnetization decay towards thermal equilibrium. Electron relaxation is similarly a stochastic process acting on the nucleus via the hyperfine coupling, and therefore will also lead to nuclear relaxation. This process is referred to as Paramagnetic Relaxation Enhancement (PRE), and manifests in a number of forms. We will investigate the impact of electron $T_1$ and $T_2$ on the nuclear $T_1$ and $T_2$ in the presence of an isotropic hyperfine coupling and a dipolar hyperfine coupling.\n", "\n", "Note that modulation of the hyperfine coupling itself also leads to forms of paramagnetic relaxation, including the [Overhauser Effect](../Chapter4/Ch4_OverhauserEffect.ipynb), which was already discussed in the DNP chapter. We will not revisit these here, but be aware that hyperfine modulation will also play a role in transverse relaxation of the nucleus. " ] } , { "cell_type": "code", "execution_count": 0, "metadata": {"tags": [ "remove-cell" ]}, "outputs": [], "source": [ "# SETUP SLEEPY\n", "import sys\n", "if 'google.colab' in sys.modules:\n", " !pip install sleepy-nmr" ] }, { "cell_type": "markdown", "id": "6787761f", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 2, "id": "34759d1b", "metadata": {}, "outputs": [], "source": [ "import SLEEPY as sl\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "sl.Defaults['verbose']=False" ] }, { "cell_type": "markdown", "id": "d64217cd", "metadata": {}, "source": [ "## PRE from an isotropic hyperfine coupling\n" ] }, { "cell_type": "markdown", "id": "29c323fc", "metadata": {}, "source": [ "### Build the system\n", "We start with an electron nuclear system, with an isotropic hyperfine coupling" ] }, { "cell_type": "code", "execution_count": 3, "id": "43e4e180", "metadata": {}, "outputs": [], "source": [ "ex=sl.ExpSys(v0H=500,Nucs=['13C','e-'],LF=True)\n", "aiso=5e5\n", "ex.set_inter(Type='hyperfine',i0=0,i1=1,Axx=aiso,Ayy=aiso,Azz=aiso) #Hyperfine coupling\n", "\n", "L=ex.Liouvillian()" ] }, { "cell_type": "markdown", "id": "28644378", "metadata": {}, "source": [ "### Electron $T_2$ relaxation only" ] }, { "cell_type": "code", "execution_count": 4, "id": "f7f9e102", "metadata": {}, "outputs": [], "source": [ "L.clear_relax()\n", "L.add_relax('T2',i=1,T2=1e-13)\n", "seq=L.Sequence(Dt=1.01e-3)\n", "\n", "rho=sl.Rho('13Cx+13Cz',['13Cp','13Cz','ez'])\n", "_=rho.DetProp(seq,n=10000)" ] }, { "cell_type": "code", "execution_count": 5, "id": "708d30f5", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho.downmix()\n", "T1=2.1\n", "ax=plt.subplots(1,2,figsize=[9,4])[1]\n", "rho.plot(axis='s',det_num=0,ax=ax[0])\n", "ax[0].set_title('$T_2$ decay')\n", "ax[0].plot(rho.t_axis,0.5*np.exp(-rho.t_axis/(T1*2)),color='black',linestyle=':')\n", "rho.plot(axis='s',det_num=[1,2],ax=ax[1])\n", "ax[1].set_title(r'$T_1$ / Overhauser effect')\n", "_=ax[1].plot(rho.t_axis,np.exp(-rho.t_axis/(T1/2))*0.5+0.5,color='black',linestyle=':')" ] }, { "cell_type": "markdown", "id": "3cefa57f", "metadata": {}, "source": [ "We see that the electron $T_2$ induces transverse relaxation on the nucleus. In fact, this is an Overhauser effect in the rotating frame (ROE), but the short electron $T_2$ immediately destroys any magnetization gained on the electron. It also induces a transfer of longitudinal magnetization between electron and nucleus. In a real system, the electron $T_1$ relaxation would almost immediately destroy the gains on the electron. However, transfer in the opposite direction allows, in principle, an Overhauser effect enhancement (although unlikely– the short electron $T_2$ used here would make electron saturation very difficult).\n", "\n", "We have plotted a monoexponential curve on each plot. For $T_1$-decay, we have a time-constant of 2.1 seconds, and for $T_2$-decay, a time-constant twice as long, of 4.2 seconds. Then, this is a rare case when $T_2$ relaxation is slower than $T_1$ relaxation (see [Traficante 1991](https://doi.org/10.1002/cmr.1820030305)). This occurs when the relaxing field, in this case the non-secular components of the hyperfine coupling, only comes in the xy-plane, where the electron $T_2$ is active. We will later see that relaxation induced by the electron $T_1$ will prevent $T_2$ from actually exceeding $T_1$ in such a system.\n", "\n", "We can evaluate the dependence of the nuclear $T_1$ on the electron $T_2$. We expect to find the minimum $T_1$ when $T_{2e}=1/|(\\omega_{0e}-\\omega_{0n})|$, i.e. matched to the energy difference of the two spins, which we will mark on the resulting plot." ] }, { "cell_type": "code", "execution_count": 6, "id": "78e83f60", "metadata": {}, "outputs": [], "source": [ "rho=sl.Rho('13Cz','13Cz')\n", "T20=np.logspace(-14,-10,100)\n", "R1=[]\n", "for T2 in T20:\n", " L.clear_relax()\n", " L.add_relax('T2',i=1,T2=T2)\n", " R1.append(rho.extract_decay_rates(L.U(Dt=1e-3)))" ] }, { "cell_type": "code", "execution_count": 7, "id": "f662503b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots()[1]\n", "ax.loglog(T20,R1)\n", "ax.set_ylim(ax.get_ylim())\n", "T2max=1/(2*np.pi*np.abs(ex.v0[0]-ex.v0[1]))\n", "ax.plot(T2max*np.ones(2),ax.get_ylim(),linestyle=':',color='black')\n", "ax.set_xlabel(r'$T_{2e}$ / s')\n", "_=ax.set_ylabel(r'$1/T_{1n}$ / s$^{-1}$')" ] }, { "cell_type": "markdown", "id": "f5dc8ac9", "metadata": {}, "source": [ "Indeed, the minimum occurs as expected (we plot $1/T_{1n}$, so this appears as a maximum), where the dashed line marks the predicted minimum." ] }, { "cell_type": "markdown", "id": "a4a61950", "metadata": {}, "source": [ "### Electron $T_1$ relaxation only" ] }, { "cell_type": "markdown", "id": "adcf5b16", "metadata": {}, "source": [ "We next observe relaxation when only electron $T_1$ is present. This is unphysical, but we do it anyway to separate the two effects. Note that SLEEPY will warn us about the unphysicality." ] }, { "cell_type": "code", "execution_count": 8, "id": "1e6650ef", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/albertsmith/Documents/GitHub/SLEEPY/SLEEPY/Liouvillian.py:499: UserWarning: T1 relaxation included without T2 relaxation. Unphysical system\n", " warnings.warn('T1 relaxation included without T2 relaxation. Unphysical system')\n" ] } ], "source": [ "L.clear_relax()\n", "L.add_relax('T1',i=1,T1=1e-13)\n", "seq=L.Sequence(Dt=1.0e-3)\n", "\n", "rho=sl.Rho('13Cx+13Cz',['13Cp','13Cz','ez'])\n", "_=rho.DetProp(seq,n=10000)" ] }, { "cell_type": "code", "execution_count": 9, "id": "dc2a4778", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho.downmix()\n", "T1=2.1\n", "ax=plt.subplots(1,2,figsize=[9,4])[1]\n", "rho.plot(axis='s',det_num=0,ax=ax[0])\n", "ax[0].set_title('$T_2$ decay')\n", "ax[0].plot(rho.t_axis,0.5*np.exp(-rho.t_axis/(T1*2)),color='black',linestyle=':')\n", "rho.plot(axis='s',det_num=[1,2],ax=ax[1])\n", "_=ax[1].set_title(r'$T_1$ / Overhauser effect')" ] }, { "cell_type": "markdown", "id": "6fc61b62", "metadata": {}, "source": [ "Then, we see that an electron $T_1$ acting via an isotropic hyperfine coupling induces $T_2$ decay, but no $T_1$ or Overhauser effect. As mentioned above, if we have electron $T_1$ and $T_2$ together, then we no longer have the case that $T_{2n}T_{2n}$.\n", "\n", "Below, we simulate the case that $T_{1e}=T_{2e}$, verifying that then $T_{1n}=T_{2n}$." ] }, { "cell_type": "code", "execution_count": 10, "id": "2ebf275c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "L.clear_relax()\n", "L.add_relax('T1',i=1,T1=1e-13)\n", "L.add_relax('T2',i=1,T2=1e-13)\n", "seq=L.Sequence(Dt=1.01e-3)\n", "\n", "rho=sl.Rho('13Cx+13Cz',['13Cp','13Cz','ez'])\n", "_=rho.DetProp(seq,n=10000)\n", "rho.downmix()\n", "T1=2.1\n", "ax=plt.subplots(1,2,figsize=[9,4])[1]\n", "rho.plot(axis='s',det_num=0,ax=ax[0])\n", "ax[0].set_title('$T_2$ decay')\n", "ax[0].plot(rho.t_axis,0.5*np.exp(-rho.t_axis/T1),color='black',linestyle=':')\n", "rho.plot(axis='s',det_num=[1,2],ax=ax[1])\n", "ax[1].plot(rho.t_axis,np.exp(-rho.t_axis/T1),color='black',linestyle=':')\n", "_=ax[1].set_title(r'$T_1$ / Overhauser effect')" ] }, { "cell_type": "markdown", "id": "b5c95e27", "metadata": {}, "source": [ "Both $T_{2n}$ and $T_{1n}$ are approximately 2.1 seconds." ] }, { "cell_type": "markdown", "id": "d9ae5d06", "metadata": {}, "source": [ "We can also acquire dependence of the nuclear $T_2$ on the electron $T_1$.\n", "\n", "This is a little tricker than extracting the $T_1$. Decay rates are extracted from the real part of the eigenvalues of the propagators, but the relevant rates are easily identified because they are non-oscillating. For $T_2$, that is no longer the case, so that we simply search for the biggest term and extract its decay rate. This is not always the correct approach for extracting decay of an oscillating signal, but works here because all the other terms are negligible." ] }, { "cell_type": "code", "execution_count": 11, "id": "bce0dd42", "metadata": {}, "outputs": [], "source": [ "rho=sl.Rho('13Cx','13Cp')\n", "T10=np.logspace(-12,-1,200)\n", "R2=[]\n", "for T1 in T10:\n", " L.clear_relax()\n", " L.add_relax('T1',i=1,T1=T1) #Longer than all T2s used\n", " L.add_relax('T2',i=1,T2=1e-12)\n", " rate,_,A=rho.extract_decay_rates(L.U(Dt=1e-6),mode='all')\n", " i=np.argmax(A[0])\n", " R2.append(rate[0][i])" ] }, { "cell_type": "code", "execution_count": 12, "id": "45c9e980", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots()[1]\n", "ax.loglog(T10,R2)\n", "ax.set_ylim(ax.get_ylim())\n", "ax.set_xlabel(r'$T_{1e}$ / s')\n", "_=ax.set_ylabel(r'$1/T_{2n}$ / s$^{-1}$')" ] }, { "cell_type": "markdown", "id": "3a8c9095", "metadata": {}, "source": [ "Then, as the electron $T_1$ gets longer, the nuclear $T_2$ gets shorter, resulting in a linear plot for short correlation times. However, when $1/T_1<2\\pi A_{iso}\\approx3x10^{-6}$ s$^{-1}$, the nuclear $T_2$ becomes longer again. A sharp transition occurs, similar to the coalescence condition found for simple [1D exchange](../Chapter2/Ch2_exchange1D.ipynb). Note that after this transition, we would observe two peaks, seen below." ] }, { "cell_type": "code", "execution_count": 13, "id": "16a05d7c", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "L.clear_relax()\n", "L.add_relax('T1',i=1,T1=5e-6)\n", "L.add_relax('T2',i=1,T2=1e-12)\n", "\n", "rho.clear()\n", "rho.DetProp(L.U(Dt=1e-7),n=1000)\n", "rho.downmix()\n", "_=rho.plot(FT=True)" ] }, { "cell_type": "markdown", "id": "b5f69e3f", "metadata": {}, "source": [ "## PRE from a dipolar hyperfine coupling" ] }, { "cell_type": "markdown", "id": "0c9cb13c", "metadata": {}, "source": [ "A dipolar hyperfine coupling will also induce paramagnetic relaxation enhancement, although the dependence of the nuclear relaxation on the electron $T_2$ and $T_1$ is different than the scalar case. We investigate this below. Note that now we use a powder-averaged system and magic angle spinning." ] }, { "cell_type": "markdown", "id": "b42ae23c", "metadata": {}, "source": [ "### Build the system" ] }, { "cell_type": "code", "execution_count": 14, "id": "810a3b44", "metadata": {}, "outputs": [], "source": [ "ex=sl.ExpSys(v0H=500,Nucs=['13C','e-'],LF=True,pwdavg=4)\n", "delta=5e5\n", "ex.set_inter(Type='hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta) #Hyperfine coupling\n", "\n", "L=ex.Liouvillian()" ] }, { "cell_type": "markdown", "id": "d4f349c6", "metadata": {}, "source": [ "### Electron $T_2$ relaxation only" ] }, { "cell_type": "code", "execution_count": 15, "id": "17d180ad", "metadata": {}, "outputs": [], "source": [ "L.clear_relax()\n", "L.add_relax('T2',i=1,T2=5e-13,OS=True)\n", "seq=L.Sequence()\n", "U=seq**20\n", "\n", "rho=sl.Rho('13Cx+13Cz',['13Cp','13Cz','ez'])\n", "_=rho.DetProp(U,n=10000)" ] }, { "cell_type": "code", "execution_count": 16, "id": "f86fded5", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho.downmix()\n", "ax=plt.subplots(1,2,figsize=[9,4])[1]\n", "rho.plot(axis='s',det_num=0,ax=ax[0])\n", "ax[0].set_title('$T_2$ decay')\n", "rho.plot(axis='s',det_num=[1,2],ax=ax[1])\n", "_=ax[1].set_title(r'$T_1$, Overhauser effect')" ] }, { "cell_type": "markdown", "id": "0876067b", "metadata": {}, "source": [ "Electron $T_2$ then similarly induces a nuclear $T_2$ and $T_1$. Unlike the scalar case, the $T_1$ is not a pure Overhauser effect transfer, and eventually the full magnetization is destroyed. " ] }, { "cell_type": "markdown", "id": "3f0edffe", "metadata": {}, "source": [ "The electron hyperfine coupling is strong enough to tilt the nuclear quantization axis away from the *z*, such that MAS can no longer average the coupling, yielding a complex lineshape if we Fourier transform the transverse magnetization. Note that this effect will only appear if the nucleus is in the lab frame." ] }, { "cell_type": "code", "execution_count": 17, "id": "df43a443", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho.apod_pars['LB']=2\n", "_=rho.plot(FT=True,det_num=0,apodize=True).set_xlim([200,-200])" ] }, { "cell_type": "markdown", "id": "73113c01", "metadata": {}, "source": [ "We can also sweep the electron $T_2$ to determine the dependence of the nuclear $T_1$ on the $T_2$." ] }, { "cell_type": "code", "execution_count": 18, "id": "ab1c6094", "metadata": {}, "outputs": [], "source": [ "# Takes a few minutes\n", "ex=sl.ExpSys(v0H=500,Nucs=['13C','e-'],LF=True,pwdavg=2)\n", "delta=5e5\n", "ex.set_inter(Type='hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta) #Hyperfine coupling\n", "\n", "L=ex.Liouvillian()\n", "\n", "rho=sl.Rho('13Cz','13Cz')\n", "T20=np.logspace(-14,-10,50)\n", "R1=[]\n", "for T2 in T20:\n", " L.clear_relax()\n", " L.add_relax('T2',i=1,T2=T2)\n", " R1.append(rho.extract_decay_rates(L.U()))" ] }, { "cell_type": "code", "execution_count": 19, "id": "dc6329a0", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots()[1]\n", "ax.loglog(T20,R1)\n", "ax.set_ylim(ax.get_ylim())\n", "T2max=1/(2*np.pi*np.abs(ex.v0[0]-ex.v0[1]))\n", "ax.plot(T2max*np.ones(2),ax.get_ylim(),linestyle=':',color='black')\n", "ax.set_xlabel(r'$T_{2e}$ / s')\n", "_=ax.set_ylabel(r'$1/T_{1n}$ / s$^{-1}$')" ] }, { "cell_type": "markdown", "id": "531ec7cf", "metadata": {}, "source": [ "As with the scalar hyperfine, we find the maximum at $T_{2e}=1/|(\\omega_{0e}-\\omega_{0n})|$." ] }, { "cell_type": "markdown", "id": "8273af45", "metadata": {}, "source": [ "### Electron $T_1$ relaxation only\n", "Above, we saw the influence of the electron $T_{2e}$ on the nuclear $T_{1n}$ and $T_{2n}$, in the presence of a dipolar hyperfine coupling. Here, we investigate the influence of the electron $T_{1e}$." ] }, { "cell_type": "code", "execution_count": 20, "id": "627c9625", "metadata": {}, "outputs": [], "source": [ "ex=sl.ExpSys(v0H=500,Nucs=['13C','e-'],LF=True,pwdavg=4)\n", "delta=5e5\n", "ex.set_inter(Type='hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta) #Hyperfine coupling\n", "\n", "L=ex.Liouvillian()" ] }, { "cell_type": "code", "execution_count": 21, "id": "101217a3", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/albertsmith/Documents/GitHub/SLEEPY/SLEEPY/Liouvillian.py:499: UserWarning: T1 relaxation included without T2 relaxation. Unphysical system\n", " warnings.warn('T1 relaxation included without T2 relaxation. Unphysical system')\n" ] } ], "source": [ "L.clear_relax()\n", "L.add_relax('T1',i=1,T1=5e-13)\n", "seq=L.Sequence()\n", "U=seq**20\n", "\n", "rho=sl.Rho('13Cx+13Cz',['13Cp','13Cz','ez'])\n", "_=rho.DetProp(U,n=10000)" ] }, { "cell_type": "code", "execution_count": 22, "id": "c5110f5e", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho.downmix()\n", "ax=plt.subplots(1,2,figsize=[9,4])[1]\n", "rho.plot(axis='s',det_num=0,ax=ax[0])\n", "ax[0].set_title('$T_2$ decay')\n", "rho.plot(axis='s',det_num=[1,2],ax=ax[1])\n", "_=ax[1].set_title(r'$T_1$, Overhauser effect')" ] }, { "cell_type": "markdown", "id": "03281bcc", "metadata": {}, "source": [ "As with the scalar hyperfine coupling, the electron $T_1$ relaxation induces $T_2$. $T_1$ relaxation is also induced on the nucleus, but without inducing any Overhauser effect. We can calculate the nuclear $T_1$ as a function of electron $T_1$, as is done below." ] }, { "cell_type": "code", "execution_count": 23, "id": "e6859f65", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/albertsmith/Documents/GitHub/SLEEPY/SLEEPY/Liouvillian.py:499: UserWarning: T1 relaxation included without T2 relaxation. Unphysical system\n", " warnings.warn('T1 relaxation included without T2 relaxation. Unphysical system')\n" ] } ], "source": [ "# Takes a few minutes\n", "ex=sl.ExpSys(v0H=500,Nucs=['13C','e-'],LF=True,pwdavg=2)\n", "delta=5e5\n", "ex.set_inter(Type='hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta) #Hyperfine coupling\n", "\n", "L=ex.Liouvillian()\n", "\n", "rho=sl.Rho('13Cz','13Cz')\n", "T10=np.logspace(-11,-7,50)\n", "R1=[]\n", "for T1 in T10:\n", " L.clear_relax()\n", " L.add_relax('T1',i=1,T1=T1)\n", " R1.append(rho.extract_decay_rates(L.U()))" ] }, { "cell_type": "code", "execution_count": 24, "id": "facc5cbf", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots()[1]\n", "ax.loglog(T10,R1)\n", "ax.set_ylim(ax.get_ylim())\n", "T2max=1/(2*np.pi*np.abs(ex.v0[0]))\n", "ax.plot(T2max*np.ones(2),ax.get_ylim(),linestyle=':',color='black')\n", "ax.set_xlabel(r'$T_{2e}$ / s')\n", "_=ax.set_ylabel(r'$(1/T_{1n})$ / s$^{-1}$')" ] }, { "cell_type": "markdown", "id": "4890e334", "metadata": {}, "source": [ "We see that the maximum occurs when $T_{1e}=1/|(\\omega_{0n})|$, in contrast to the results from the scalar hyperfine coupling where no nuclear $T_{1n}$ was induced by the electron $T_{1e}$" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 5 }